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Author: Shanti S. Gupta Publisher: ISBN: Category : Languages : en Pages : 24
Book Description
In most practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, in one-way ANOVA the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means theta sub 7 ..., theta sub K are not all equal, would by itself usually be insufficient to satisfy the experimenter. In fact his problems would begin at this stage. The experimenter may desire to select the best population or a subset of the good populations; he may like to rank the populations in order of goodness or he may like to draw some other inferences about the parameters of interest. The extensive literature on selection and ranking procedures depends heavily on the use of independence between populations (block, treatments, etc.) in the analysis of variance. In the present paper, a method was derived to construct locally best (in some sense) selection procedures to select a non empty subset of the k populations containing the best population as ranked in terms of theta sub 1's which control the size of the selected subset and which maximizes the probability of selecting the best. Also considered was the usual selection procedures in one-way ANOVA based on the generalized least squares estimates and apply the method to two-way layout case.
Author: Shanti S. Gupta Publisher: ISBN: Category : Languages : en Pages : 24
Book Description
In most practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, in one-way ANOVA the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means theta sub 7 ..., theta sub K are not all equal, would by itself usually be insufficient to satisfy the experimenter. In fact his problems would begin at this stage. The experimenter may desire to select the best population or a subset of the good populations; he may like to rank the populations in order of goodness or he may like to draw some other inferences about the parameters of interest. The extensive literature on selection and ranking procedures depends heavily on the use of independence between populations (block, treatments, etc.) in the analysis of variance. In the present paper, a method was derived to construct locally best (in some sense) selection procedures to select a non empty subset of the k populations containing the best population as ranked in terms of theta sub 1's which control the size of the selected subset and which maximizes the probability of selecting the best. Also considered was the usual selection procedures in one-way ANOVA based on the generalized least squares estimates and apply the method to two-way layout case.
Author: S. S. Gupta Publisher: Springer Science & Business Media ISBN: 1461259258 Category : Mathematics Languages : en Pages : 113
Book Description
The theory and practice of decision making involves infinite or finite number of actions. The decision rules with a finite number of elements in the action space are the so-called multiple decision procedures. Several approaches to problems of multi ple decisions have been developed; in particular, the last decade has witnessed a phenomenal growth of this field. An important aspect of the recent contributions is the attempt by several authors to formalize these problems more in the framework of general decision theory. In this work, we have applied general decision theory to develop some modified principles which are reasonable for problems in this field. Our comments and contributions have been written in a positive spirt and, hopefully, these will an impact on the future direction of research in this field. Using the various viewpoints and frameworks, we have emphasized recent developments in the theory of selection and ranking ~Ihich, in our opinion, provides one of the main tools in this field. The growth of the theory of selection and ranking has kept apace with great vigor as is evidenced by the publication of two recent books, one by Gibbons, Olkin and Sobel (1977), and the other by Gupta and Panchapakesan (1979). An earlier monograph by Bechhofer, Kiefer and Sobel (1968) had also provided some very interest ing work in this field.
Author: Richard Park Bland Publisher: ISBN: Category : Analysis of variance Languages : en Pages : 196
Book Description
The problem of choosing the largest of n means is considered as a multiple decision problem which is generated from n component two-decision problems. With additive losses Bayes rules for the component problems yield Bayes rules for the multiple decision problem. Some properties of these Bayes rules are found. Also a co servativenear-Bayes rule is presented with tabled values for any number of means. (Author).
Author: Shanti S. Gupta Publisher: SIAM ISBN: 0898715326 Category : Mathematics Languages : en Pages : 592
Book Description
An encyclopaedic coverage of the literature in the area of ranking and selection procedures. It also deals with the estimation of unknown ordered parameters. This book can serve as a text for a graduate topics course in ranking and selection. It is also a valuable reference for researchers and practitioners.
Author: Deng-Yuan Huang Publisher: ISBN: Category : Languages : en Pages : 78
Book Description
The report makes some contributions to the subset selection procedures - both for the fixed sample and the sequential case. Chapter 1 deals with some subset selection procedures for binomial populations in terms of the entropy functions, which is different from the usual selection problem in terms of the success probabilities. In Chapter 2, some fixed sample optimal subset selection procedures are discussed for model I and II problems in the analysis of variance in treatments versus control, and a method for constructing some subset selection procedures is derived. Chapter 3 discusses a method for constructing some sequential subset selection procedures and some optimal sequential subset selection procedure in treatments versus control. An upper bound on the expected sample size for Bechhofer-Kiefer-Sobel sequential selection procedure with indifference zone approach is also derived. (Author).
Author: Y. L. Tong Publisher: Academic Press ISBN: 1483269213 Category : Mathematics Languages : en Pages : 256
Book Description
Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.
Author: Ronald Christensen Publisher: CRC Press ISBN: 9780412062919 Category : Mathematics Languages : en Pages : 608
Book Description
This text presents a comprehensive treatment of basic statistical methods and their applications. It focuses on the analysis of variance and regression, but also addressing basic ideas in experimental design and count data. The book has four connecting themes: similarity of inferential procedures, balanced one-way analysis of variance, comparison of models, and checking assumptions. Most inferential procedures are based on identifying a scalar parameter of interest, estimating that parameter, obtaining the standard error of the estimate, and identifying the appropriate reference distribution. Given these items, the inferential procedures are identical for various parameters. Balanced one-way analysis of variance has a simple, intuitive interpretation in terms of comparing the sample variance of the group means with the mean of the sample variance for each group. All balanced analysis of variance problems are considered in terms of computing sample variances for various group means. Comparing different models provides a structure for examining both balanced and unbalanced analysis of variance problems and regression problems. Checking assumptions is presented as a crucial part of every statistical analysis. Examples using real data from a wide variety of fields are used to motivate theory. Christensen consistently examines residual plots and presents alternative analyses using different transformation and case deletions. Detailed examination of interactions, three factor analysis of variance, and a split-plot design with four factors are included. The numerous exercises emphasize analysis of real data. Senior undergraduate and graduate students in statistics and graduate students in other disciplines using analysis of variance, design of experiments, or regression analysis will find this book useful.
Author: Shanti S. Gupta
Author: Shanti S. Gupta
Author: S. S. Gupta
Author: Richard Park Bland
Author: Shanti S. Gupta
Author: 
Author: Deng-Yuan Huang
Author: Y. L. Tong
Author: Ronald Christensen
Author: Shanti S. Gupta
Author: R. E. Bechhoefer