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This is the final report on Contract DAAG-29-77-C-0003 entitled 'Multiple-Decision Selection and Ranking Procedures.' The report lists the technical reports and published papers (and those accepted for or submitted for publication) which were written with the full or partial support of the contract. Also included is a list of the scientific personnel supported by the contract, and the advanced degrees earned by them while supported by the contract. Some general comments are made concerning research progress and implementation of findings. (Author)

Battlespace Management systems are often developed by decomposing the problem into separate functions. For example, the battle scene is decomposed into intelligence reports, sensor displays for each sensor, contact tracks for each sensor contact, environmental (weather, oceanography) conditions and predictions, sensor effectiveness predictions, geophysical/ physical oceanographic pictures, etc. Once the problem has been decomposed and analyzed, the decision maker must put it back together in a mental information fusion process, integrating information. The tools to help the expert decision maker re-fuse the problem are far fewer and more difficult to develop than the tools to decompose. The research reported here takes an alternative approach by providing information displays that cluster and integrate information according to the expert decision maker's knowledge schema and procedural structure. A complex, time-dependant (but non-military) test domain with multiple conflicting goals was selected. Functional partitioning required greater effort while procedurally based information-clustering resulted in more efficient (timely and accurate) decision making.

A resurgence of interest in multiple hypothesis testing has occurred in the last decade. Motivated by studies in genomics, microarrays, DNA sequencing, drug screening, clinical trials, bioassays, education and psychology, statisticians have been devoting considerable research energy in an effort to properly analyze multiple endpoint data. In response to new applications, new criteria and new methodology, many ad hoc procedures have emerged. The classical requirement has been to use procedures which control the strong familywise error rate (FWE) at some predetermined level \alpha. That is, the probability of any false rejection of a true null hypothesis should be less than or equal to \alpha. Finding desirable and powerful multiple test procedures is difficult under this requirement. One of the more recent ideas is concerned with controlling the false discovery rate (FDR), that is, the expected proportion of rejected hypotheses which are, in fact, true. Many multiple test procedures do control the FDR. A much earlier approach to multiple testing was formulated by Lehmann [Ann. Math. Statist. 23 (1952) 541-552 and 28 (1957) 1-25]. Lehmann's approach is decision theoretic and he treats the multiple endpoints problem as a 2^k finite action problem when there are k endpoints. This approach is appealing since unlike the FWE and FDR criteria, the finite action approach pays attention to false acceptances as well as false rejections.

This is the final report on Contract DAAG29-73-C-0008 entitled Multiple-Decision Selection and Ranking Procedures. The report lists the technical reports and published papers (and those accepted for or submitted for publication) which were written with the full or partial support of the contract. Also included is a list of the scientific personnel supported by the contract, and the advanced degrees earned by them while supported by the contract. Some general comments are made concerning research progress and implementation of findings. (Author)

Selection and ranking (more broadly multiple decision) problems arise in many practical situations since it is now well-recognized that the classical tests of homogeneity usually do not provide the answers the experimenter wants. This thesis studies Tukey's lambda distributions as the underlying model for selection and ranking problems. It is known that the family of Tukey's generalized lambda distributions is very broad and contains most well-known distributions as special cases. Chapter 1 deals with selection and ranking problems based on sample medians for the symmetric lambda distributions and gives applications of the lambda family distributions. In Chapter 2, the problems of isotonic selection procedures for the family of lambda distributions and for logistic distributions are considered. Chapter 3 deals with the problem of choosing the optimal score function for different nonparametric procedures proposed by Nagel (1970) and Gupta and McDonald (1970). A Monte Carlo study is carried out. In Chapter 4, a two-stage elimination-type procedure under the Bayesian setting is proposed and its properties are studied. In particular, we use a stopping rule to construct a 100(1-2 alpha)% Highest Posterior Density Credible regions with a common width 2d for the unknown means of selected populations at stage 1. A Monte Carlo study is carried out to examine the performance of the proposed procedure.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

The following statistical multiple-decision problems are considered for a multivariate normal distribution with unknown (or partially known) covariance matrix, using the indifference-zone and subset approaches: (a) Selecting the variate with the largest population mean; (b) selecting the variate with the smallest population variance; (c) selecting the subclass of variates with the smallest population generalized variance; (d) selecting the population with the smallest vector coefficient of alienation between two subclasses of variates; (e) selecting the best subclass of predictors for a specified subclass of variates. Small-sample theory is employed in (a) and (b), while large-sample theory is used in (b), (c), (d) and (e). (Author)

The following statistical multiple-decision problems are considered for a multivariate normal distribution with unknown (or partially known) covariance matrix, using the indifference-zone and subset approaches: (a) Selecting the variate with the largest population mean; (b) selecting the variate with the smallest population variance; (c) selecting the subclass of variates with the smallest population generalized variance; (d) selecting the population with the smallest vector coefficient of alienation between two subclasses of variates; (e) selecting the best subclass of predictors for a specified subclass of variates. Small-sample theory is employed in (a) and (b), while large-sample theory is used in (b), (c), (d) and (e). (Author)

Suppose k independent populations are given and we are interested in t (1 or = t k) of these populations which are better than the rest. Two different formulations, namely testing t slippages, and selection of a subset (of a random size or a fixed size t) containing the t better populations, are considered herein. Both of these formulations provide answers to certain relevant questions which are not answered by the classical tests of homogeneity.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

We consider testing of the homogeneity hypothesis in the one-way ANOVA model and testing for the significance of regression in the multiple linear regression model. Unlike in the classical approach, there is no alternative hypothesis to accept when the null hypothesis is rejected. When there is a substantial deviation from the null hypothesis we reject the null hypothesis and also identify the independent variables or the levels that contributed most towards the deviation from the null hypothesis.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

Monte Carlo computations of decision error probabilities for chain pooling and variations for fractional factorial experiments

Let pi sub 1,..., pi sub k represent k ( or = 2) independent populations. The quality of the ith population pi sub i is characterized by a real-valued parameter theta sub i, usually unknown. Define the best population in terms of a measure of separation between theta sub i's. A selection of a subset containing the best population is called a correct selection (CS). Restrict attention to rules for which the size of the selected subset is controlled at a given point and the infimum of the probability of correct selection over the parameter space is maximized. The main theorem deals with construction of an essentially complete class of selection rules of the above type. Some classical subset selection rules are shown to belong to this class.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

The report is a survey of developments and significant results in the area of multiple decision procedures under the subset selection formulation. Section 2 deals with procedures for location and scale parameters. A general theory of the subset selection problem and a decision-theoretic formulation are discussed in Section 3. Sections 4 through 7 deal with parametric and non- parametric procedures for discrete populations, multinomial cells and multivariate normal populations using single-stage sampling, inverse sampling and sequential sampling. Section 8 describes procedures applicable to restricted families of distributions such as the increasing failure rate (IFR) and increasing failure rate on the average (IFRA) distributions. Bayes and empirical Bayes procedures are discussed in Section 9. The last section summarizes briefly several modifications of the basic problem and goal.

The report lists the technical reports and published papers concerning 'Multiple-Decision Selection and Ranking Procedures', which were written with the full or partial support of the contract.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.

This report lists papers that deal with research on the subject of 'Statistical multiple-decision ranking and selection procedures,' a statistical methodology pioneered by the Principal Investigator and several colleagues; some of the papers deal with related statistical techniques. Interest in this subject continues to grow as is evidenced by the large number of published papers in this area, and by the appearance in the last few years of three textbooks devoted exclusively to this subject.