Downloads & Free Reading Options - Results

Bootstrap methods are widely used for distribution estimation, although in some problems they are applicable only with difficulty. A case in point is that of estimating the distributions of eigenvalue estimators, or of functions of those estimators, when one or more of the true eigenvalues are tied. The $m$-out-of-$n$ bootstrap can be used to deal with problems of this general type, but it is very sensitive to the choice of $m$. In this paper we propose a new approach, where a tie diagnostic is used to determine the locations of ties, and parameter estimates are adjusted accordingly. Our tie diagnostic is governed by a probability level, $\beta$, which in principle is an analogue of $m$ in the $m$-out-of-$n$ bootstrap. However, the tie-respecting bootstrap (TRB) is remarkably robust against the choice of $\beta$. This makes the TRB significantly more attractive than the $m$-out-of-$n$ bootstrap, where the value of $m$ has substantial influence on the final result. The TRB can be used very generally; for example, to test hypotheses about, or construct confidence regions for, the proportion of variability explained by a set of principal components. It is suitable for both finite-dimensional data and functional data.

Bootstrap methods for estimating the long-run covariance of stationary functional time series are considered. We introduce a versatile bootstrap method that relies on functional principal component analysis, where principal component scores can be bootstrapped by maximum entropy. Two other bootstrap methods resample error functions, after the dependence structure being modeled linearly by a sieve method or nonlinearly by a functional kernel regression. Through a series of Monte-Carlo simulation, we evaluate and compare the finite-sample performances of these three bootstrap methods for estimating the long-run covariance in a functional time series. Using the intraday particulate matter (PM10) data set in Graz, the proposed bootstrap methods provide a way of constructing the distribution of estimated long-run covariance for functional time series.

Bootstrap methods for estimating the long-run covariance of stationary functional time series are considered. We introduce a versatile bootstrap method that relies on functional principal component analysis, where principal component scores can be bootstrapped by maximum entropy. Two other bootstrap methods resample error functions, after the dependence structure being modeled linearly by a sieve method or nonlinearly by a functional kernel regression. Through a series of Monte-Carlo simulation, we evaluate and compare the finite-sample performances of these three bootstrap methods for estimating the long-run covariance in a functional time series. Using the intraday particulate matter (PM10) data set in Graz, the proposed bootstrap methods provide a way of constructing the distribution of estimated long-run covariance for functional time series.

We show that, when the double bootstrap is used to improve performance of bootstrap methods for bias correction, techniques based on using a single double-bootstrap sample for each single-bootstrap sample can be particularly effective. In particular, they produce third-order accuracy for much less computational expense than is required by conventional double-bootstrap methods. However, this improved level of performance is not available for the single double-bootstrap methods that have been suggested to construct confidence intervals or distribution estimators.

Several problems in variable selection and decision trees were solved. In the case of linear regression models with increasing number of covariates, a method based on ordering the covariates in terms of their t-statistics is shown to be asymptotically consistent as the sample size increases. This result holds for the fixed design situation as well as that of random covariates. A new unbiased method of split selection for classification trees was developed and implemented into computer software. The method is unbiased in the sense that when all the covariates are unrelated to the response variable, each covariate has an equal chance of being selected to split a node. No previous algorithm has this property. Bootstrap calibration plays a critical role in the algorithm. Empirical evaluations of the algorithm show that it is as accurate as the best classifiers from the statistical and computer science literature. It has the additional benefit of being one of the fastest algorithms.

Some years ago, B. Efron and his colleagues developed bootstrap resampling methods as a way of estimating the degree to which statistical results will replicate across variations in sample. A basic problem in the multivariate use of bootstrap procedures involves the requirement that the results across resamplings must be rotated to best fit in a common factor space before any estimators are averaged. The use of factor analysis for this problem is demonstrated using the responses of 298 persons to items from the Bem Sex-Role Inventory from a study by B. Thompson (1988). The statistical computer program FACSTRAP is used to calculate bootstrap confidence intervals in factor analysis. Bootstrap methods are valuable because they: (1) lend credibility to the factor analysts' choice of the number of factors to extract and interpret; (2) provide evidence for increased confidence in the interpretation of factor meaning; and (3) demonstrate the importance of replication in the social sciences. There are 9 tables of analysis results and a 35-item list of references. (SLD)

The the look down shoot down scenario, the next generation of air to surface missiles will rely on IR sensors and advanced signal processing to detect small (or point) targets in highly cluttered and noisy environments. In this paper; we present a novel wavelet detection algorithm which incorporates adaptive CFAR detection statistics using the bootstrap method. Following detection, the estimate of interframe optical flow is made using synthetic discriminant filters (SDF's). The detection coupled with the new optical flow estimate will enable higher performance in tracking small maneuverable targets. Results for the wavelet bootstrap detection are presented and compared to a conventional matched filter.

The following problems are studied and their solutions found. Bootstrap methods for confidence interval estimation of a binomial parameter and for model selection in linear regression. Tree-structured algorithms for classification, piecewise-linear regression and generalized linear models, and proportional hazards regression for censored observations. Asymptotic efficiency of tests following data transformations. Identification of significant effects from unreplicated two-level factorial designed experiments. Bounds on the asymptotic size of the likelihood ratio test of independence in a cross-classified table. (AN)

To use control charts in practice, the in-control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured for example by the false alarm probability or the average run length. We suggest an adjustment of the monitoring schemes to overcome these problems. It guarantees, with a certain probability, a conditional performance given the estimated in-control state. The suggested method is based on bootstrapping the data used to estimate the in-control state. The method applies to different types of control charts, and also works with charts based on regression models, survival models, etc. If a nonparametric bootstrap is used, the method is robust to model errors. We show large sample properties of the adjustment. The usefulness of our approach is demonstrated through simulation studies.

In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity. In contrast, the proposed methods exploit certain structural properties of a large class of massive data sets to break up the original problem into a set of simpler subproblems, solve each subproblem separately where the data exhibit approximate uniformity and where computational complexity can be reduced to a manageable level, and then combine the results through certain analytical considerations. The validity of the proposed methods is proved and their finite sample properties are studied through a moderately large simulation study. The methodology is illustrated with a real data example from Transportation Engineering, which motivated the development of the proposed methods.

This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning methods. We demonstrate empirically that the proposed bootstrap bias correction can lead to substantial improvements in both bias and predictive accuracy. In the context of ensembles of trees, we show that this correction can be approximated at only double the cost of training the original ensemble without introducing additional variance. Our method is shown to improve test-set accuracy over random forests by up to 70\% on example problems from the UCI repository.

Developed by B. Efron (1979) and his colleagues (P. Diaconis and B. Efron, 1983), bootstrap methods have the goal of creating an empirical sampling distribution that can be used to test statistical hypotheses, estimate standard errors, and create confidence intervals. Bootstrapping methods offer a unique and effective method for testing the stability and replicability of results. This paper explains the bootstrap method of exploring replicability internally, including a heuristic example applying bootstrap methods to a confirmatory factor analysis, using the Statistical Package for the Social Sciences and AMOS. (Contains 1 figure, 5 tables, and 13 references.) (Author/SLD)

This article is from BMC Neuroscience , volume 15 . Abstract Background: Pairwise association between neurons is a key feature in understanding neural coding. Statistical neuroscience provides tools to estimate and assess these associations. In the mammalian brain, activating ascending pathways arise from neuronal nuclei located at the brainstem and at the basal forebrain that regulate the transition between sleep and awake neuronal firing modes in extensive regions of the cerebral cortex, including the primary visual cortex, where neurons are known to be selective for the orientation of a given stimulus. In this paper, the estimation of neural synchrony as a function of time is studied in data obtained from anesthetized cats. A functional data analysis of variance model is proposed. Bootstrap statistical tests are introduced in this context; they are useful tools for the study of differences in synchrony strength regarding 1) transition between different states (anesthesia and awake), and 2) affinity given by orientation selectivity. Results: An analysis of variance model for functional data is proposed for neural synchrony curves, estimated with a cross-correlation based method. Dependence arising from the experimental setting needs to be accounted for. Bootstrap tests allow the identification of differences between experimental conditions (modes of activity) and between pairs of neurons formed by cells with different affinities given by their preferred orientations. In our test case, interactions between experimental conditions and preferred orientations are not statistically significant. Conclusions: The results reflect the effect of different experimental conditions, as well as the affinity regarding orientation selectivity in neural synchrony and, therefore, in neural coding. A cross-correlation based method is proposed that works well under low firing activity. Functional data statistical tools produce results that are useful in this context. Dependence is shown to be necessary to account for, and bootstrap tests are an appropriate method with which to do so.

This article is from BMC Neuroscience , volume 15 . Abstract Background: Pairwise association between neurons is a key feature in understanding neural coding. Statistical neuroscience provides tools to estimate and assess these associations. In the mammalian brain, activating ascending pathways arise from neuronal nuclei located at the brainstem and at the basal forebrain that regulate the transition between sleep and awake neuronal firing modes in extensive regions of the cerebral cortex, including the primary visual cortex, where neurons are known to be selective for the orientation of a given stimulus. In this paper, the estimation of neural synchrony as a function of time is studied in data obtained from anesthetized cats. A functional data analysis of variance model is proposed. Bootstrap statistical tests are introduced in this context; they are useful tools for the study of differences in synchrony strength regarding 1) transition between different states (anesthesia and awake), and 2) affinity given by orientation selectivity. Results: An analysis of variance model for functional data is proposed for neural synchrony curves, estimated with a cross-correlation based method. Dependence arising from the experimental setting needs to be accounted for. Bootstrap tests allow the identification of differences between experimental conditions (modes of activity) and between pairs of neurons formed by cells with different affinities given by their preferred orientations. In our test case, interactions between experimental conditions and preferred orientations are not statistically significant. Conclusions: The results reflect the effect of different experimental conditions, as well as the affinity regarding orientation selectivity in neural synchrony and, therefore, in neural coding. A cross-correlation based method is proposed that works well under low firing activity. Functional data statistical tools produce results that are useful in this context. Dependence is shown to be necessary to account for, and bootstrap tests are an appropriate method with which to do so.

The bootstrap program for 1+1-dimensional integrable Quantum Field Theories (QFT's) is developed to a large extent for the Homogeneous sine-Gordon (HSG) models. This program can be divided into various steps, which include the computation of the exact S-matrix, Form Factors of local operators and correlation functions, as well as the identification of the operator content of the QFT and the development of various consistency checks. Taking as an input the S-matrix proposal for the HSG-models, we confirm its consistency by carrying out both a Thermodynamic Bethe Ansatz (TBA) and a Form Factor analysis. In contrast to many other 1+1-dimensional integrable models studied in the literature, the HSG-models break parity, both at the level of the Lagrangian and S-matrix, and their spectrum includes unstable particles. These features have specific consequences in our analysis which are given a physical interpretation. By exploiting the Form Factor approach, we develop further the QFT advocated to the HSG-models. We evaluate correlation functions of various local operators of the model as well as Zamolodchikov's c-function and $\Delta$-sum rules. For the $SU(3)_2$-HSG model we show how the form factors of different local operators are interrelated by means of the momentum space cluster property. We find closed formulae for all $n$-particle form factors of a large class of operators of the $SU(N)_2$-HSG models. These formulae are expressed in terms of universal building blocks which allow both a determinant and an integral representation.

Many online experiments exhibit dependence between users and items. For example, in online advertising, observations that have a user or an ad in common are likely to be associated. Because of this, even in experiments involving millions of subjects, the difference in mean outcomes between control and treatment conditions can have substantial variance. Previous theoretical and simulation results demonstrate that not accounting for this kind of dependence structure can result in confidence intervals that are too narrow, leading to inaccurate hypothesis tests. We develop a framework for understanding how dependence affects uncertainty in user--item experiments and evaluate how bootstrap methods that account for differing levels of dependence perform in practice. We use three real datasets describing user behaviors on Facebook --- user responses to ads, search results, and News Feed stories --- to generate data for synthetic experiments in which there is no effect of the treatment on average by design. We then estimate empirical Type I error rates for each bootstrap method. Accounting for dependence within a single type of unit (i.e., within-user dependence) is often sufficient to get reasonable error rates. But when experiments have effects, as one might expect in the field, accounting for multiple units with a multiway bootstrap can be necessary to get close to the advertised Type I error rates. This work provides guidance to practitioners evaluating large-scale experiments, and highlights the importance of analysis of inferential methods for dependence structures common to online systems.

This thesis contains three main parts, which are largely independent. In the first part we deal with the boundary bootstrap in supersymmetric factorized scattering theory. We give a description of supersymmetry in the case when the space is a half-line and present rules for the determination of the representations in which higher level boundary bound states transform, and for the determination of the supersymmetric one-particle reflection matrix factors for the higher level boundary bound states. These rules apply under the condition that the bulk particles transform in the kink or in the boson-fermion representation. Examples for the application of these rules to specific models are also given. In the second part we investigate the problem whether the TCSA spectrum can be approximated by the spectrum of the original Hamiltonian operator in which the coefficients of the terms are suitably changed. The investigation is done in the case of the critical Ising model on a strip with an external magnetic field on one of the boundaries. Another truncation method that preserves the solvability of the model is also considered. The results of perturbative and numerical calculations show that the above approximation is possible and that the qualitative behaviour of the truncated spectrum as a function of the coupling constant depends on the truncation method. In the third part we investigate the phase structure of the two- and three-frequency sine-Gordon models using the TCSA. In the case of the three-frequency model the tricritical point, several points of the critical line and a few points of the line of first order transition are found.

We characterize the statistical bootstrap for the estimation of information-theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately, the underlying axiomatic relationships of information theory---in particular, consistency under arbitrary coarse-graining---that motivate use of these quantities in the first place, while providing reliability comparable to the state of the art for Bayesian estimators. We show how information-theoretic quantities allow for rigorous empirical study of the decision-making capacities of rational agents and the time-asymmetric flows of information in distributed systems. We provide illustrative examples by reference to ongoing collaborative work on the semantic structure of the British Criminal Court system and the conflict dynamics of the contemporary Afghanistan insurgency.

Astroparticle experiments such as IceCube or MAGIC require a deconvolution of their measured data with respect to the response function of the detector to provide the distributions of interest, e.g. energy spectra. In this paper, appropriate uncertainty limits that also allow to draw conclusions on the geometric shape of the underlying distribution are determined using bootstrap methods, which are frequently applied in statistical applications. Bootstrap is a collective term for resampling methods that can be employed to approximate unknown probability distributions or features thereof. A clear advantage of bootstrap methods is their wide range of applicability. For instance, they yield reliable results, even if the usual normality assumption is violated. The use, meaning and construction of uncertainty limits to any user-specific confidence level in the form of confidence intervals and levels are discussed. The precise algorithms for the implementation of these methods, applicable for any deconvolution algorithm, are given. The proposed methods are applied to Monte Carlo simulations to show their feasibility and their precision in comparison to the statistical uncertainties calculated with the deconvolution software TRUEE.

The objectives of this paper are two-fold. One is to report results of extensive Monte Carlo simulations which demonstrate the behavior of the mean squared error of the kernel estimator with respect to bandwidth. These simulations provide a method of choosing an optimal bandwidth when the form of the lifetime and censoring distributions are known. Also, they compare the kernel-type estimator with the product-limit qauntile estimator. Five commonly used parametric lifetime distributions, two censoring mechanisms, and four different kernel functions are considered in this study, which is an extension of the brief simulations for exponential distributions reported by Padgett (1986). The second objective is to present a nonparametric method for bandwidth selection based on the bootstrap for right-censored data. This data-based procedure used the bootstrap to estimate mean squared error, and is both an extension and modification of the methods proposed by Padgett. Bandwidth selection using the bootstrap is important for small and moderately large samples since no exact expressions exist for the mean squared error of the kernel-type quantile estimator.

The objectives of this paper are two-fold. One is to report results of extensive Monte Carlo simulations which demonstrate the behavior of the mean squared error of the kernel estimator with respect to bandwidth. These simulations provide a method of choosing an optimal bandwidth when the form of the lifetime and censoring distributions are known. Also, they compare the kernel-type estimator with the product-limit qauntile estimator. Five commonly used parametric lifetime distributions, two censoring mechanisms, and four different kernel functions are considered in this study, which is an extension of the brief simulations for exponential distributions reported by Padgett (1986). The second objective is to present a nonparametric method for bandwidth selection based on the bootstrap for right-censored data. This data-based procedure used the bootstrap to estimate mean squared error, and is both an extension and modification of the methods proposed by Padgett. Bandwidth selection using the bootstrap is important for small and moderately large samples since no exact expressions exist for the mean squared error of the kernel-type quantile estimator.

It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample distribution of SVMs by the bootstrap approach.

It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample distribution of SVMs by the bootstrap approach.

Statistical significance is often inappropriately equated with evaluating result importance and evaluating result replicability, even though these are three somewhat different issues. The prudent researcher must separately assess each of these elements of the "research triumvirate" by using different methods. This paper focuses on two types of empirical methods for estimating research result replicability: double cross-validation, and bootstrap procedures. A commonly available statistical computer package, the Statistical Package for the Social Sciences (SPSS-X), is used to carry out the steps required for the double cross-validation procedure, and a recently developed microcomputer program package (developed by C. E. Lunneborg, 1987) is implemented to demonstrate the bootstrap logic. Both methods are applied to a heuristic data set of observed values of three independent variables and one dependent variable for a sample of 25 subjects. It is concluded that although each procedure has some shortcomings, the advantages of using either far outweigh the disadvantages. There are 5 tables of analysis data and a 19-item list of references. (SLD)