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A single linear vertical passive array is used in the 'SOFAR' channel to determine the depth of a single underwater source at a constant range. The phase and amplitude weights applied to the array are determined by the linear minimum variance estimation technique. The resulting beam pattern is compared to the conventional time domain beamformer. It was found that the linear minimum variance estimation technique of amplitude shading and phase weighting was significantly superior to the conventional beamformer. (Author)

A computer program has been developed for the Maximum Likelihood estimation of parameters in general non-linear systems. Sensitivity matrix elements are calculated numerically, overcoming the need for explicit sensitivity equations. Parameters such as break points and time shifts are successfully determined using both simulated and actual test data. Keywords: Non linear systems, Time lag, Drop tests, Parameter estimation, Maximum likelihood, Landing gear.

We consider a power-constrained sensor network, consisting of multiple sensor nodes and a fusion center (FC), that is deployed for the purpose of estimating a common random parameter of interest. In contrast to the distributed framework, the sensor nodes are allowed to update their individual observations by (linearly) combining observations from neighboring nodes. The updated observations are communicated to the FC using an analog amplify-and-forward modulation scheme and through a coherent multiple access channel. The optimal collaborative strategy is obtained by minimizing the cumulative transmission power subject to a maximum distortion constraint. For the distributed scenario (i.e., with no observation sharing), the solution reduces to the power-allocation problem considered by [Xiao, TSP08]. Collaboration among neighbors significantly improves power efficiency of the network in the low local-SNR regime, as demonstrated through an insightful example and numerical simulations.

In a series of papers the author developed two approaches towards a unified treatment of the General Gauss-Markoff (GGM) linear model (Y, X beta, sigma squared V) where V, the dispersion matrix of Y, may be singular and X may be deficient in rank. One is called the inverse partition (IPM) method which depends on the numerical evaluation of a g-inverse of a partitioned matrix. Another is an analogue of least square theory and is called unified least square (ULS) method. The aim of the paper is to bring out the salient features of these two methods and to point out some interesting features of linear unbiased estimation when the dispersion matrix of the observations is singular.

This paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of regularization-induced confounding is introduced, which refers to the tendency of regularization priors to adversely bias treatment effect estimates by over-shrinking control variable regression coefficients. Then, a simultaneous regression model is presented which permits regularization priors to be specified in a way that avoids this unintentional re-confounding. The new model is illustrated on synthetic and empirical data.

The notion of approximately integrable linear statistical models is introduced to analyze the higher order optimality properties of some common nonparametric estimators. The approximately integrable models suggest a useful approach to a unified treatment of both regular and irregular non-parameter problems. It is shown that with such models any rate of improvement ranging from (log n) to the alpha power/squared to 1/(log...log n) to the alpha power), alpha 0, of the classical non-parametric procedures can be anticipated. Both an example of a first order asymptotically optimal estimator with the unusual rate 1/n log n and an estimator with an extremely slow unimprovable rate of convergence 1(log...log n) the alpha power are presented.

Recent advances in observational techniques related to geodetic work (VLBI, laser ranging) make it imperative that more consideration should be given to modeling problems. Uncertainties in the effect of atmospheric refraction, polar motion and precession-nutation parameters, cannot be dispensed with in the context of centimeter level geodesy. Even physical processes that have generally been previously altogether neglected (station motions) must now be taken into consideration. The problem of modeling functions of time or space, or at least their values at observation points (epochs) is explored. When the nature of the function to be modeled is unknown. The need to include a limited number of terms and to a priori decide upon a specific form may result in a representation which fails to sufficiently approximate the unknown function. An alternative approach of increasing application is the modeling of unknown functions as stochastic processes.

In the past two decades since the advent of Kalman's recursive filter, numerous algorithms for linear estimation have emerged. Most of these algorithms are recursive and rely on solving a Riccati equation or equivalent recursive equations. It will be shown how some of the classical problems such as Linear Smoothing and Recursive Block Filtering problems can be solved exactly by some new nonrecursive algorithms which are based on the Fast Fourier Transform (FFT). Moreover, these algorithms are readily modified to generate the Riccati matrix at specified times, if this is desired. These results are then extended to a block filtering algorithm, where data is received and smoothed recursively block by block. Real time batch processing applications include image processing and array processing of signals.

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with respect to the $\mathbb{L}_p$ loss. An application to the problem of estimating a signal or its $r^{th}$ derivative at a given point is developed and minimax rates are proved to hold uniformly over Besov balls. We also apply our non asymptotic oracle inequality to the estimation of the mean of the signal on an interval with length depending on the noise level. Simulations are included to illustrate the performances of the procedure for the estimation of a function at a given point. Our method provides a pointwise adaptive estimator.

In this paper we investigate a problem of state estimation for the dynamical system described by the linear operator equation with unknown parameters in Hilbert space. We present explicit expressions for linear minimax estimation and error provided that any pair of uncertain parameters belongs to the quadratic bounding set. As an application of the main result we present the solution of minimax estimation problem for the linear descriptor differential equation with constant matrices.

The purpose of the current study was to examine whether log-linear smoothing of observed score distributions in small samples results in more accurate differential item functioning (DIF) estimates under the simultaneous item bias test (SIBTEST) framework. Data from a teacher certification test were analyzed using White candidates in the reference group and African American candidates in the focal group. Smoothed and raw DIF estimates from 100 replications under seven different sample-size conditions were compared to a criterion to determine the effect of smoothing on small-sample DIF estimation. Root-mean-squared deviation and bias were used to evaluate the accuracy of DIF detection in the smoothed versus raw data conditions. Results indicate that, for most studied items, smoothing the raw score distributions reduced variability and bias of the DIF estimates especially in the small-sample-size conditions. Implications of these results for actual testing programs and future directions for research are discussed.

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We consider a significant generalization in which the relationship between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$ is noisy, quantized to a single bit, potentially nonlinear, noninvertible, as well as unknown. This model is known as the single-index model in statistics, and, among other things, it represents a significant generalization of one-bit compressed sensing. We propose a novel spectral-based estimation procedure and show that we can recover $\beta^*$ in settings (i.e., classes of link function $f$) where previous algorithms fail. In general, our algorithm requires only very mild restrictions on the (unknown) functional relationship between $y_i$ and $\langle \mathbf{x}_i,\beta^* \rangle$. We also consider the high dimensional setting where $\beta^*$ is sparse ,and introduce a two-stage nonconvex framework that addresses estimation challenges in high dimensional regimes where $p \gg n$. For a broad class of link functions between $\langle \mathbf{x}_i,\beta^* \rangle$ and $y_i$, we establish minimax lower bounds that demonstrate the optimality of our estimators in both the classical and high dimensional regimes.

A unified approach is developed for the estimation of unknown fixed parameters and prediction of random effects in a mixed Gauss-Markoff linear model. It is shown that both the estimators and their mean square errors can be expressed in terms of the elements of a g-inverse of a partitioned matrix which can be set up in terms of the matrices used in expressing the model. No assumptions are made on the ranks of the matrices involved. The method is parallel to the one developed by the author in the case of the fixed effects Gauss-Markoff model using a g-inverse of a partitioned matrix. A new concept of generalized normal equations is introduced for the simultaneous estimation of fixed parameters, random effects and random error. All the results are deduced from a general lemma on an optimization problem. This paper is self contained as all the algebraic results used are stated and proved. The unified theory developed in an earlier paper (Rao, 1988) is somewhat simplified.

Several ways for detection and assessment of collinearity in measured data are discussed. Because data collinearity usually results in poor least squares estimates, two estimation techniques which can limit a damaging effect of collinearity are presented. These two techniques, the principal components regression and mixed estimation, belong to a class of biased estimation techniques. Detection and assessment of data collinearity and the two biased estimation techniques are demonstrated in two examples using flight test data from longitudinal maneuvers of an experimental aircraft. The eigensystem analysis and parameter variance decomposition appeared to be a promising tool for collinearity evaluation. The biased estimators had far better accuracy than the results from the ordinary least squares technique.

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a nonexistent MLE. Our conditions focus on the role of sampling zeros in the observed table. We situate our results within the framework of extended exponential families, and we exploit the geometric properties of log-linear models. We propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log-linear model analysis.

Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with Gaussian predictors. We obtain sharp asymptotics for the minimax risk that are applicable in any asymptotic setting where the number of predictors diverges and prove that ridge regression is asymptotically minimax. Adaptive asymptotic minimax ridge estimators are also identified. Orthogonal invariance is heavily exploited throughout the paper and, beyond serving as a technical tool, provides additional insight into the problems considered here. Most of our results follow from an apparently novel analysis of an equivalent non-Gaussian sequence model with orthogonally invariant errors. As with many dense estimation and prediction problems, the minimax risk studied here has rate d/n, where d is the number of predictors and n is the number of observations; however, when d is roughly proportional to n the minimax risk is influenced by the spectral distribution of the predictors and is notably different from the linear minimax risk for the Gaussian sequence model (Pinsker, 1980) that often appears in other dense estimation and prediction problems.

The paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field. We consider linear distributed estimators whose structure combines the information \emph{flow} among sensors (the \emph{consensus} term resulting from the local gossiping exchange among sensors when they are able to communicate) and the information \emph{gathering} measured by the sensors (the \emph{sensing} or \emph{innovations} term.) This leads to mixed time scale algorithms--one time scale associated with the consensus and the other with the innovations. The paper establishes a distributed observability condition (global observability plus mean connectedness) under which the distributed estimates are consistent and asymptotically normal. We introduce the distributed notion equivalent to the (centralized) Fisher information rate, which is a bound on the mean square error reduction rate of any distributed estimator; we show that under the appropriate modeling and structural network communication conditions (gossip protocol) the distributed gossip estimator attains this distributed Fisher information rate, asymptotically achieving the performance of the optimal centralized estimator. Finally, we study the behavior of the distributed gossip estimator when the measurements fade (noise variance grows) with time; in particular, we consider the maximum rate at which the noise variance can grow and still the distributed estimator being consistent, by showing that, as long as the centralized estimator is consistent, the distributed estimator remains consistent.

Introduction [1] Arabi sheep population includes almost 55% of the local sheep population in Khuzestan province. Lamb mortality is a universal problem in sheep breeding that may be reached to 20-40% of total lambs born and could impact the genetic improvement, animal welfare and economic viability of sheep breeding, adversely. Research on improving survival of lambs is likely to have a higher pay-off than research on improving the number of lambs conceived. Lamb survival is a compound trait affected by many various factors related to climate, management, lamb and ewe behavior and genetic effects. Lamb survivability is controlled by genetics of the animal, contributed by direct genetic and maternal effects and also by environmental effects. There are disagreements among researchers about using a suitable model to analyze the survival traits, and each researcher has suggested the use of specific models. In general, the use of linear and threshold models has been suggested for survival trait analysis. Although survival has great economic importance, in the studies conducted on Iranian livestock, less attention has been paid to it. The aim of this study was to analyze the genetic parameters for the survival of Arabi lambs from birth to one year of age using linear and Weibull models. Materials and Methods in this study, 5452 lamb survival records collected by the Jahad Agricultural Organization of Ahvaz from 1993 to 2005 were used. Traits included were cumulative survival from birth to the end of one year and on a monthly basis. In order to estimate genetic parameters using linear models, the Restricted Maximum Likelihood (REML) method was used in Wombat software based on a univariate analysis. The Weibull model and Matvec software were also used for estimating variance component and genetic parameters of Survival rate. Results and Discussion Different models compared using the likelihood ratio test. For survival traits until 1, 4, 5, and 10 months, the model 4 was suitable, which include the direct additive genetic effect, maternal additive genetic effect and their covariance. In the case of until 2 months, the best model was the model 3, which include the direct and maternal additive genetic effects. For until 3, 8, 9, and 12 months, model 1 including direct additive genetic effect was selected. And for other traits Model 5 (direct additive genetic, maternal additive genetic, and maternal permanent environmental effects) was chosen as the best model. The direct heritability of survival rate estimated from different linear models was in the range of 0.025 to 0.061. In general, despite the high economic importance of survival in the breeds until one year of age, due to low estimates of the inheritance of these traits using linear models, it cannot be expected that genetic selection alone can make significant genetic progress. The genetic variance component among sires, heritability on the logarithmic scale, heritability on the original scale, and effective heritability obtained from Weibull sire model were increased to a peak point at 4 months. After that, a decline occurred until 5 months, and then a fluctuation was observed until 9 months. A limited increase was found in the 11 and 12 months. The heritability of sire model, in the logarithmic scale, had a low to medium range (0.13-0.25), and in the original scale had a medium to high range (0.39-0.75). The effective heritability was estimated in the medium range. Estimated values of the survival heritability using the Weibull model was greater than the value obtained from the linear animal model. Although heritability estimations for survival and mortality is low, it is possible that genetic progress may be enhanced by selecting lambs with higher breeding value for survival. Conclusion Estimation of the genetic parameters for survival lambs from birth to one year of age using linear and Weibull models were low vs medium to high, respectively. Therefore, based on the results of linear models, response to   direct selection to improve the survival of lambs in this breed will be very slow, and more attention should be paid to improving non-genetic factors and indirect selection and outbreeding, but based on The results of Weibull models, it seems that the rate of response to genetic selection to improve survival trait is faster using these models compared to the linear models, suggest that lamb survival could be improved   through direct selection and could be included in the Arabi sheep selection   index.  

For a general link linear model (GLLM), we show that the OLS estimate of the slope vector is strongly consistent up to a multiplicative scale, even though the model might actually be nonlinear. Furthermore, the estimated slope vector is strongly consistent for the average slope vector, the average of the pointwise slope vectors on the response surface. For a GLLM with a completely specified link function, we can solve for the multiplicative scalar and estimate the intercept and Cox and Snell's generalized residuals. We then estimate the response surface and the pointwise slopes using a generalization of the smearing estimate in Duan (1983). The results can be applied to a number of important subclasses of GLLM, including general transformation models, general scaled transformation models, dichotomous regression, and Tobit regression.

The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.

There are no author-identified significant results in this report.

We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.

It is well-known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct this problem, Nishida and Kanazawa (2015) proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall (1998) proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of one LL estimator and two SK estimators that are symmetrically placed on both sides of the LL estimator (the convex combination (CC) estimator) to eliminate higher-order terms in its asymptotic bias. To obtain a CC estimator with a constant estimator variance without employing the VS local variable bandwidth, the weight in the convex combination must be determined locally to produce a constant estimator variance. In this study, we compare the performances of two VS methods for a CC estimator and find cases in which the weighting method can superior to the VS bandwidth method in terms of the degree of variance stabilization.

In this paper we consider the problem of estimating simultaneously low-rank and row-wise sparse matrices from nested linear measurements where the linear operator consists of the product of a linear operator $\mathcal{W}$ and a matrix $\mathbf{\varPsi}$. Leveraging the nested structure of the measurement operator, we propose a computationally efficient two-stage algorithm for estimating the simultaneously structured target matrix. Assuming that $\mathcal{W}$ is a restricted isometry for low-rank matrices and $\mathbf{\varPsi}$ is a restricted isometry for row-wise sparse matrices, we establish an accuracy guarantee that holds uniformly for all sufficiently low-rank and row-wise sparse matrices with high probability. Furthermore, using standard tools from information theory, we establish a minimax lower bound for estimation of simultaneously low-rank and row-wise sparse matrices from linear measurements that need not be nested. The accuracy bounds established for the algorithm, that also serve as a minimax upper bound, differ from the derived minimax lower bound merely by a polylogarithmic factor of the dimensions. Therefore, the proposed algorithm is nearly minimax optimal. We also discuss some applications of the proposed observation model and evaluate our algorithm through numerical simulation.

Two new methods for estimation of parameters in log-linear models are proposed and their properties considered in this article. Conditions for the existence of the new estimators are derived, and the new estimators are shown to possess appropriate asymptotic properties.

The discrete Wiener matrix equation is solved for the case of a complex bandlimited (BL) signal corrupted by additive lowpass correlated noise. The solution is achieved by the method of undetermined coefficients which significantly reduces the dimensionality of the problem. Asymptotic properties of the minimum mean-square error (MMSE) weight vector solutions are examined for the cases of very long filter lengths and degeneration to white noise. These special cases allow the MMSE filter impulse response to be examined in terms of its noise and signal components. It is then shown that by proper choice of prediction distance Delta, one may remove much of the noise effects upon the MMSE filter while retaining the desired BL signal characteristics. (Author)

Understanding the concepts of spectral estimation may become increasingly important in future radar system design. The purpose of this technical memo is to introduce these concepts. A simple model is formulated using a uniformly spaced linear phased array, and the classical Fourier, Maximum Entropy (ME), and Multiple Signal Classification (MUSIC) techniques are described. The performance of these three techniques is discussed through qualitative comparison.

A simple differential equation for the triangular square-root of the error covariance of the linear state estimator is derived. Previous algorithms involved an antisymmetric matrix in the square-root differential equation. In the constant model case, Chandrasekhar-type equations are shown to constitute a set of fast square-root algorithms for the derivative of the error variance. Square-Root algorithms for the smoothing problem are presented and as in the discrete case, an array method for handling continuous square-roots is developed. This method also yields very naturally the usual normalizations of stochastic calculus, suggesting extensions to more general stochastic equations, even to estimators for nonlinear models. (Author)

This article is from BMC Medical Research Methodology , volume 11 . Abstract Background: Log-linear association models have been extensively used to investigate the pattern of agreement between ordinal ratings. In 2007, log-linear non-uniform association models were introduced to estimate, from a cross-classification of two independent raters using an ordinal scale, varying degrees of distinguishability between distant and adjacent categories of the scale. Methods: In this paper, a simple method based on simulations was proposed to estimate the power of non-uniform association models to detect heterogeneities across distinguishabilities between adjacent categories of an ordinal scale, illustrating some possible scale defects. Results: Different scenarios of distinguishability patterns were investigated, as well as different scenarios of marginal heterogeneity within rater. For sample size of N = 50, the probabilities of detecting heterogeneities within the tables are lower than .80, whatever the number of categories. In additition, even for large samples, marginal heterogeneities within raters led to a decrease in power estimates. Conclusion: This paper provided some issues about how many objects had to be classified by two independent observers (or by the same observer at two different times) to be able to detect a given scale structure defect. Our results also highlighted the importance of marginal homogeneity within raters, to ensure optimal power when using non-uniform association models.

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution, and suppose that $f$ is $\mathrm{OPT}$-close in $L_1$-distance to an unknown piecewise polynomial function with $t$ interval pieces and degree $d$. Our algorithm draws $n = O(t(d+1)/\epsilon^2)$ samples from $f$, runs in time $\tilde{O}(n \cdot \mathrm{poly}(d))$, and with probability at least $9/10$ outputs an $O(t)$-piecewise degree-$d$ hypothesis $h$ that is $4 \cdot \mathrm{OPT} +\epsilon$ close to $f$. Our general algorithm yields (nearly) sample-optimal and nearly-linear time estimators for a wide range of structured distribution families over both continuous and discrete domains in a unified way. For most of our applications, these are the first sample-optimal and nearly-linear time estimators in the literature. As a consequence, our work resolves the sample and computational complexities of a broad class of inference tasks via a single "meta-algorithm". Moreover, we experimentally demonstrate that our algorithm performs very well in practice. Our algorithm consists of three "levels": (i) At the top level, we employ an iterative greedy algorithm for finding a good partition of the real line into the pieces of a piecewise polynomial. (ii) For each piece, we show that the sub-problem of finding a good polynomial fit on the current interval can be solved efficiently with a separation oracle method. (iii) We reduce the task of finding a separating hyperplane to a combinatorial problem and give an efficient algorithm for this problem. Combining these three procedures gives a density estimation algorithm with the claimed guarantees.

This investigation considers a non-linear technique for extracting natural resonances from transient electromagnetic scattering responses of radar targets. These natural resonances represent the complex poles of the target's transfer function in the Laplace transform s-plane. The advantage of their use in identification is their dependence only upon the geometry and composition of the target and not upon the aspect and polarization of the incident signal. Based on recent theoretical research, a new signal model has been developed for describing the form of the transient scattering response. This form precludes the optimal use of previous methods for natural resonance extraction based on Prony's algorithm. In this effort, a modified least-squares approach is taken which can accommodate the actual form of the transient signal. The algorithm is tested using simulated signals with various noise levels and conclusions are drawn concerning the viability of the method. (Author)

This paper presents a method to determine end members along with their relative concentration in a hyperspectral mixed pixel. The method is modeled as a linear combination of the end members reflectance spectra and a library of spectral prototypes. This method was tested with 431-band, laboratory controlled, data sets. Indications are that this method can be extended to field data observations with a small number of end members and that at least some error source can be identified and data and results adjusted accordingly.

This paper presents a method to determine end members along with their relative concentration in a hyperspectral mixed pixel. The method is modeled as a linear combination of the end members reflectance spectra and a library of spectral prototypes. This method was tested with 431-band, laboratory controlled, data sets. Indications are that this method can be extended to field data observations with a small number of end members and that at least some error source can be identified and data and results adjusted accordingly.

This report describes results of research on factorial designs during a two-year period ending in February 1965. These include (a) characterizations of orthogonal and two classes of non-orthogonal designs as solutions to linear constraints, (b) optimality properties of orthogonal designs, (c) development of a general class of non-orthogonal sequential factorial designs, (d) results on certain families of 2(n) designs, and (e) description of a special-purpose linear programming computer routine for combinatorial problems in experimental design. (Author)

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth+singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain precise error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.

Robust estimates for the parameters in the general linear model are proposed which are based on weighted rank statistics. The method is based on the minimization of a dispersion function defined by a weighted Gini's mean difference. An asymptotic distribution of the estimate is derived. Some examples are discussed which point out that the ranking can be based on a restricted set of comparisons and still retain high efficiency. (Author)

One of the problems considered in the report is to find the vector of weights W minimizing E the set((d(t)-W(sup T)X(T))) quantity squared subject to linear equality constraints on W, where X(t) is a vector of random variables measured at time t and d(t) is a random variable related to X(t). This is a classical problem in linear estimation theory, except that the statistics of the random variables are assumed unknown and must be learned through observations. The other problem considered is in the classical design of processors for sensor arrays whose purpose is signal detection and estimation, a receiver is optimized on the basis of the a prior knowledge of the statistics of its input signals. However, when the a priori knowledge is not available, the receiver's performance can still be improved by performing measurements on its input signals and incorporating this new information into its design. Such receivers are called adaptive. The purpose of this research is to develop and analyze a gradient-descent surface-searching algorithm for automatically adjusting (adapting) the parameters of a linear tapped-delay-line array processor in order to improve its performance in an unknown changing environment.

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the regression framework or the inverse problem framework, a data-driven model selection criterion is obtained either under general assumptions, or under the mild assumption of model identifiability respectively. The proposed approach was stimulated by the important recent non-asymptotic model selection results due to Birg\'e and Massart mainly (Birge and Massart 2007), and our results in this paper, like theirs, are non-asymptotic and turn to be sharp. Our main contribution in this paper resides in the fact that these linear estimators are not necessarily least-squares estimators but can be any linear estimators. The proposed approach finds therefore potential applications in countless fields of engineering and applied science (image science, signal processing,applied statistics, coding, to name a few) in which one is interested in recovering some unknown vector quantity of interest as the one, for example, which achieves the best trade-off between a term of fidelity to data, and a term of regularity or/and parsimony of the solution. The proposed approach provides then such applications with an interesting model selection framework that allows them to achieve such a goal.

This paper considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, $n$, and the number of time periods, $T$, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when $n$ and $T$ jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is $O(T^{-1})$, and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either $(nT)^{-1/2}$ or $n^{-1/2}$. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.

We offer a new Monte-Carlo method for solving of linear integral equation which gives the unbiased estimation for solution of Volterra's and Fredholm's type, and consider the problem of confidence region building. We study especially the case of the so-called equations with weak singularity in the kernel of Abelian type.

In a linear transformation model, there exists an unknown monotone nonlinear transformation function such that the transformed response variable and the predictor variables satisfy a linear regression model. In this paper, we present CENet, a new method for estimating the slope vector and simultaneously performing variable selection in the high-dimensional sparse linear transformation model. CENet is the solution to a convex optimization problem and can be computed efficiently from an algorithm with guaranteed convergence to the global optimum. We show that under a pairwise elliptical distribution assumption on each predictor-transformed-response pair and some regularity conditions, CENet attains the same optimal rate of convergence as the best regression method in the high-dimensional sparse linear regression model. To the best of our limited knowledge, this is the first such result in the literature. We demonstrate the empirical performance of CENet on both simulated and real datasets. We also discuss the connection of CENet with some nonlinear regression/multivariate methods proposed in the literature.

We study estimation of regression parameters in heteroscedastic linear models when the number of parameters is large. The results generalize work of Huber (1973), Yohai and Maronna (1979), and Ruppert and Carroll (1989). (Author)

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is suitable for more complicated data structures. However, its estimation inherits the difficulties and complexities from both components and makes it a challenging problem, which calls for new methodology. We propose a novel profile B-spline method to estimate the parameters by approximating the unknown nonparametric link function in the single-index component part with B-spline, while the linear slope function in the functional component part is estimated by the functional principal component basis. The consistency and asymptotic normality of the parametric estimators are derived, and the global convergence of the proposed estimator of the linear slope function is also established. More excitingly, the latter convergence is optimal in the minimax sense. A two-stage procedure is implemented to estimate the nonparametric link function, and the resulting estimator possesses the optimal global rate of convergence. Furthermore, the convergence rate of the mean squared prediction error for a predictor is also obtained. Empirical properties of the proposed procedures are studied through Monte Carlo simulations. A real data example is also analyzed to illustrate the power and flexibility of the proposed methodology.

For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main object of interest is the class s-sparse vectors for which we also provide completely adaptive estimators (independent of s and of the noise variance) having only logarithmically slower rates than the minimax ones. Furthermore, we obtain the minimax rates on the Lq-balls where 0 < q < 2. This analysis shows that there are, in general, three zones in the rates of convergence that we call the sparse zone, the dense zone and the degenerate zone, while a fourth zone appears for estimation of the quadratic functional. We show that, as opposed to estimation of the vector, the correct logarithmic terms in the optimal rates for the sparse zone scale as log(d/s^2) and not as log(d/s). For the sparse class, the rates of estimation of the linear functional and of the L2-norm have a simple elbow at s = sqrt(d) (boundary between the sparse and the dense zones) and exhibit similar performances, whereas the estimation of the quadratic functional reveals more complex effects and is not possible only on the basis of sparsity described by the sparsity condition on the vector. Finally, we apply our results on estimation of the L2-norm to the problem of testing against sparse alternatives. In particular, we obtain a non-asymptotic analog of the Ingster-Donoho-Jin theory revealing some effects that were not captured by the previous asymptotic analysis.

This article is from Journal of Medical Physics / Association of Medical Physicists of India , volume 38 . Abstract The measured dose in water at reference point in phantom is a primary parameter for planning the treatment monitor units (MU); both in conventional and intensity modulated/image guided treatments. Traceability of dose accuracy therefore still depends mainly on the calibration factor of the ion chamber/dosimeter provided by the accredited Secondary Standard Dosimetry Laboratories (SSDLs), under International Atomic Energy Agency (IAEA) network of laboratories. The data related to Nd,water calibrations, thermoluminescent dosimetry (TLD) postal dose validation, inter-comparison of different dosimeter/electrometers, and validity of Nd,water calibrations obtained from different calibration laboratories were analyzed to find out the extent of accuracy achievable. Nd,w factors in Gray/Coulomb calibrated at IBA, GmBH, Germany showed a mean variation of about 0.2% increase per year in three Farmer chambers, in three subsequent calibrations. Another ion chamber calibrated in different accredited laboratory (PTW, Germany) showed consistent Nd,w for 9 years period. The Strontium-90 beta check source response indicated long-term stability of the ion chambers within 1% for three chambers. Results of IAEA postal TL “dose intercomparison” for three photon beams, 6 MV (two) and 15 MV (one), agreed well within our reported doses, with mean deviation of 0.03% (SD 0.87%) (n = 9). All the chamber/electrometer calibrated by a single SSDL realized absorbed doses in water within 0.13% standard deviations. However, about 1-2% differences in absorbed dose estimates observed when dosimeters calibrated from different calibration laboratories are compared in solid phantoms. Our data therefore imply that the dosimetry level maintained for clinical use of linear accelerator photon beams are within recommended levels of accuracy, and uncertainties are within reported values.

Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.

This report considers the multivariate linear regression model X = F1 Xi F2 +E, where X is a c x N matrix of observations, F1 is a known c x p matrix of covariates, F2 is a known m x N design matrix (containing values of independent variables in the regression), and XI is an unknown p x m matrix of regression coefficients assumed under a null hypothesis H0 to satisfy a system of linear restraints of the form H0: U1 Xi F3 = ab, where F3: m x k and b: s x h are known matrices, and U1: r x p and alpha: r x s (s or = r or = p) are unknown matrices of restraint coefficients. The error matrix E: c x N is assumed to have columns which are statistically independent, multivariate normal random vectors with common mean vector 0 and common unknown matrix sigma.

This research presents the method of Linear Regression as a parameter identification method to determine the longitudinal dimensional stability derivatives of a tactical missile. Missile flight histories are characterized by rapid accelerations, rapidly changing mass property characteristics with often short flight times. These characteristics make accurate parameter estimation of the missile aerodynamics more challenging than for aircraft. The simulation used for this research was created in MATLAB/SIMULINK based on the missile trajectory program, TRAP. The aerodynamic data for the 6- DoF missile model was based on a supersonic, tail controlled missile similar to an AIM-9X missile. Two command input types were investigated for excitation of the system modes. This research shows that linear regression can be used successfully in determining longitudinal dimensional stability derivatives of a tactical missile in flight when using a control input form with higher frequency modulations, such as band-limited or filtered white noise.

A robust procedure for location and/or scale parameter estimation is presented which utilizes the (asymptotically best linear unbiased estimators) (ABLUE's) based on k(less than N) of the N sample quantiles. Using regression design techniques a method is developed for selecting sample quantiles which furnishes the corresponding parameter estimates with good robustness properties relative to a given finite set of known probability laws. The problems of robust quantile selection for the estimation of a particular population quantile or in the presence of left and/or right hand censoring are also considered.

A hierarchical latent regression model is suggested to estimate nested and nonnested relationships in complex samples such as found in the National Assessment of Educational Progress (NAEP). The proposed model aims at improving both parameters and variance estimates via a two-level hierarchical linear model. This model falls naturally within the set of models used in most large scale surveys, in that all of them are special cases of the hierarchical latent regression model. The model parameter estimates are obtained via the expectation-maximization (EM) algorithm. An example with NAEP data is presented and results of parameter estimation and standard errors are compared with results from operational procedures of NAEP.