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Author: Ricardo Milton Frischtak Publisher: ISBN: Category : Multivariate analysis Languages : en Pages : 226
Book Description
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).
Author: Ricardo Milton Frischtak Publisher: ISBN: Category : Multivariate analysis Languages : en Pages : 226
Book Description
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).
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: Arjun K. Gupta Publisher: Springer Science & Business Media ISBN: 9401706530 Category : Mathematics Languages : en Pages : 392
Book Description
The death of Professor K.C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog nition of his many contributions in multivariate statis tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T.C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J.D. Knoke, W.J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D.K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.
Author: Nitis Mukhopadhyay Publisher: CRC Press ISBN: 9780824790783 Category : Mathematics Languages : en Pages : 434
Book Description
"This useful volume provides a thorough synthesis of second-order asymptotics in multistage sampling methodologies for selection and ranking unifying available second-order results in general and applying them to a host of situations Contains, in each chapter, helpful Notes and Overviews to facilitate comprehension, as well as Complements and Problems for more in-depth study of specific topics!"
Author: Jean Dickinson Gibbons Publisher: SIAM ISBN: 9781611971101 Category : Mathematics Languages : en Pages : 594
Book Description
This SIAM Classics edition is an unabridged, corrected republication of the work first published in 1977. It provides a compendium of applied aspects of ordering and selection procedures and includes tables that permit the practitioner to carry out the experiment and draw statistically justified conclusions. These tables are not readily available in other texts. Although more than 1000 papers and several books on the general theory of ranking and selection have been published since this book first appeared, the methodology is presented in a more elementary fashion, with numerous examples to help the reader apply it to a specific problem. There is a dichotomy in modern statistics that distinguishes between analyses done before an experiment is completed and those done afterward. Ranking and selection methods are useful in both of these categories. The authors provide an alternative to the overused "testing the null hypothesis" when what the practitioner really needs is a method of ranking k given populations, selecting the t best populations, or some similar goal. That need and purpose is as important today as when the subject was first developed nearly 50 years ago.
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: 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: Ricardo Milton Frischtak
Author: Ricardo Milton Frischtak
Author: Shanti S. Gupta
Author: Arjun K. Gupta
Author: Nitis Mukhopadhyay
Author: Jean Dickinson Gibbons
Author: Y. L. Tong
Author: 
Author: S. S. Gupta
Author: 
Author: Yung Liang Tong