Multiple Statistical Decision Theory Recent Developments

Author : S. S. Gupta,D.-Y. Huang
Publisher : Springer
Page : 104 pages
File Size : 44,9 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 1461259266

Get Book

Multiple Statistical Decision Theory: Recent Developments by S. S. Gupta,D.-Y. Huang Pdf

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 : Shanti Swarup Gupta,Deng-Yuan Huang
Publisher : Unknown
Page : 104 pages
File Size : 52,9 Mb
Release : 1981
Category : Analyse séquentielle - Statistique mathématique
ISBN : 3540905723

Get Book

Multiple Statistical Decision Theory by Shanti Swarup Gupta,Deng-Yuan Huang Pdf

Some auxiliary results: monotonicity properties of probability distributions; Multiple decision theory: a general approach; Modified minimax decision procedures; Invariant decision procedures; Robust selection procedures: most economical multiple decision rules; Multiple decision procedures based on tests.

Author : S. S. Gupta,D.-Y. Huang
Publisher : Springer Science & Business Media
Page : 113 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461259251

Get Book

Multiple Statistical Decision Theory: Recent Developments by S. S. Gupta,D.-Y. Huang Pdf

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 : Silvia Bacci,Bruno Chiandotto
Publisher : CRC Press
Page : 217 pages
File Size : 54,8 Mb
Release : 2019-07-11
Category : Mathematics
ISBN : 9781351621380

Get Book

Introduction to Statistical Decision Theory by Silvia Bacci,Bruno Chiandotto Pdf

Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory

Author : S. Panchapakesan,N. Balakrishnan
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461223085

Get Book

Advances in Statistical Decision Theory and Applications by S. Panchapakesan,N. Balakrishnan Pdf

Shanti S. Gupta has made pioneering contributions to ranking and selection theory; in particular, to subset selection theory. His list of publications and the numerous citations his publications have received over the last forty years will amply testify to this fact. Besides ranking and selection, his interests include order statistics and reliability theory. The first editor's association with Shanti Gupta goes back to 1965 when he came to Purdue to do his Ph.D. He has the good fortune of being a student, a colleague and a long-standing collaborator of Shanti Gupta. The second editor's association with Shanti Gupta began in 1978 when he started his research in the area of order statistics. During the past twenty years, he has collaborated with Shanti Gupta on several publications. We both feel that our lives have been enriched by our association with him. He has indeed been a friend, philosopher and guide to us.

Author : Shanti S. Gupta,James O. Berger
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461226185

Get Book

Statistical Decision Theory and Related Topics V by Shanti S. Gupta,James O. Berger Pdf

The Fifth Purdue International Symposium on Statistical Decision The was held at Purdue University during the period of ory and Related Topics June 14-19,1992. The symposium brought together many prominent leaders and younger researchers in statistical decision theory and related areas. The format of the Fifth Symposium was different from the previous symposia in that in addition to the 54 invited papers, there were 81 papers presented in contributed paper sessions. Of the 54 invited papers presented at the sym posium, 42 are collected in this volume. The papers are grouped into a total of six parts: Part 1 - Retrospective on Wald's Decision Theory and Sequential Analysis; Part 2 - Asymptotics and Nonparametrics; Part 3 - Bayesian Analysis; Part 4 - Decision Theory and Selection Procedures; Part 5 - Probability and Probabilistic Structures; and Part 6 - Sequential, Adaptive, and Filtering Problems. While many of the papers in the volume give the latest theoretical developments in these areas, a large number are either applied or creative review papers.

Author : F. Liese,Klaus-J. Miescke
Publisher : Springer Science & Business Media
Page : 696 pages
File Size : 54,6 Mb
Release : 2008-12-30
Category : Mathematics
ISBN : 9780387731940

Get Book

Statistical Decision Theory by F. Liese,Klaus-J. Miescke Pdf

For advanced graduate students, this book is a one-stop shop that presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner, while observing statistical relevance. All of the major topics are introduced at an elementary level, then developed incrementally to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. With its broad coverage of decision theory, this book fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.

Author : Shanti S. Gupta,James O. Berger
Publisher : Academic Press
Page : 550 pages
File Size : 41,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483259550

Get Book

Statistical Decision Theory and Related Topics III by Shanti S. Gupta,James O. Berger Pdf

Statistical Decision Theory and Related Topics III, Volume 2 is a collection of papers presented at the Third Purdue Symposium on Statistical Decision Theory and Related Topics, held at Purdue University in June 1981. The symposium brought together many prominent leaders and a number of younger researchers in statistical decision theory and related areas. This volume contains the research papers presented at the symposium and includes works on general decision theory, multiple decision theory, optimum experimental design, sequential and adaptive inference, Bayesian analysis, robustness, and large sample theory. These research areas have seen rapid developments since the preceding Purdue Symposium in 1976, developments reflected by the variety and depth of the works in this volume. Statisticians and mathematicians will find the book very insightful.

Author : Norbert Schmitz
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227366

Get Book

Optimal Sequentially Planned Decision Procedures by Norbert Schmitz Pdf

Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8» turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential Analysis" ([Wa]*) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayes optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.

Author : K. Balakrishnan
Publisher : Routledge
Page : 414 pages
File Size : 52,6 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351449113

Get Book

Exponential Distribution by K. Balakrishnan Pdf

The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon

Author : Solomon Kullback,John C. Keegel,Joseph H. Kullback
Publisher : Springer Science & Business Media
Page : 169 pages
File Size : 42,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461580805

Get Book

Topics in Statistical Information Theory by Solomon Kullback,John C. Keegel,Joseph H. Kullback Pdf

The relevance of information theory to statistical theory and its applications to stochastic processes is a unifying influence in these TOPICS. The integral representation of discrimination information is presented in these TOPICS reviewing various approaches used in the literature, and is also developed herein using intrinsically information-theoretic methods. Log likelihood ratios associated with various stochastic processes are computed by an application of minimum discrimination information estimates. Linear discriminant functionals are used in the information-theoretic analysis of a variety of stochastic processes. Sections are numbered serially within each chapter, with a decimal notation for subsections. Equations, examples, theorems and lemmas, are numbered serially within each section with a decimal notation. The digits to the left of the decimal point represent the section and the digits to the right of the decimal point the serial number within the section. When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given. References to the bibliography are by the author's name followed by the year of publication in parentheses. The transpose of a matrix is denoted by a prime; thus one-row matrices are denoted by primes as the transposes of one-column matrices (vectors).

Author : J. Pfanzagl
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257691

Get Book

Contributions to a General Asymptotic Statistical Theory by J. Pfanzagl Pdf

Author : Y. Kharin
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 46,8 Mb
Release : 1996-09-30
Category : Mathematics
ISBN : 0792342674

Get Book

Robustness in Statistical Pattern Recognition by Y. Kharin Pdf

This book is concerned with important problems of robust (stable) statistical pat tern recognition when hypothetical model assumptions about experimental data are violated (disturbed). Pattern recognition theory is the field of applied mathematics in which prin ciples and methods are constructed for classification and identification of objects, phenomena, processes, situations, and signals, i. e. , of objects that can be specified by a finite set of features, or properties characterizing the objects (Mathematical Encyclopedia (1984)). Two stages in development of the mathematical theory of pattern recognition may be observed. At the first stage, until the middle of the 1970s, pattern recogni tion theory was replenished mainly from adjacent mathematical disciplines: mathe matical statistics, functional analysis, discrete mathematics, and information theory. This development stage is characterized by successful solution of pattern recognition problems of different physical nature, but of the simplest form in the sense of used mathematical models. One of the main approaches to solve pattern recognition problems is the statisti cal approach, which uses stochastic models of feature variables. Under the statistical approach, the first stage of pattern recognition theory development is characterized by the assumption that the probability data model is known exactly or it is esti mated from a representative sample of large size with negligible estimation errors (Das Gupta, 1973, 1977), (Rey, 1978), (Vasiljev, 1983)).

Author : Masanobu Taniguchi
Publisher : Springer Science & Business Media
Page : 169 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461231547

Get Book

Higher Order Asymptotic Theory for Time Series Analysis by Masanobu Taniguchi Pdf

The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.

Author : Martin A. Tanner
Publisher : Springer Science & Business Media
Page : 118 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Medical
ISBN : 9781468405101

Get Book

Tools for Statistical Inference by Martin A. Tanner Pdf

From the reviews: The purpose of the book under review is to give a survey of methods for the Bayesian or likelihood-based analysis of data. The author distinguishes between two types of methods: the observed data methods and the data augmentation ones. The observed data methods are applied directly to the likelihood or posterior density of the observed data. The data augmentation methods make use of the special "missing" data structure of the problem. They rely on an augmentation of the data which simplifies the likelihood or posterior density. #Zentralblatt für Mathematik#