Multiple Statistical Decision Theory Recent Developments
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| Author | : S. S. Gupta |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 113 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461259258 |
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 | : S. Panchapakesan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 478 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461223083 |
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 | : Silvia Bacci |
| Publisher | : CRC Press |
| Total Pages | : 305 |
| Release | : 2019-07-11 |
| Genre | : Mathematics |
| ISBN | : 1351621394 |
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 | : Shanti S. Gupta |
| Publisher | : Academic Press |
| Total Pages | : 551 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483259552 |
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 | : F. Liese |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 696 |
| Release | : 2008-12-30 |
| Genre | : Mathematics |
| ISBN | : 0387731946 |
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 | : Kuldeep Kumar |
| Publisher | : Universal-Publishers |
| Total Pages | : 205 |
| Release | : 2012 |
| Genre | : Business & Economics |
| ISBN | : 161233573X |
This book is part of the proceedings of The International Conference on Recent Developments in Statistics, Econometrics and Forecasting 2010, which was organized to provide opportunities for academics and researchers to share their knowledge on recent developments in this area. The conference featured the most up-to-date research results and applications in statistics, econometrics and forecasting. The book has fifteen chapters contributed by different authors and can be divided into five parts: Time Series and Econometric Modeling, Linear Models, Non-parametrics, Statistical Applications and Statistical Methodology. This book will be helpful to graduate students, researchers and applied statisticians working in the area of time series, statistical and econometric modeling.
| Author | : H. Tong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468478885 |
In the last two years or so, I was most fortunate in being given opportunities of lecturing on a new methodology to a variety of audiences in Britain, China, Finland, France and Spain. Despite my almost Confucian attitude of preferring talking (i.e. a transient record) to writing (i.e. a permanent record), the warm encouragement of friends has led to the ensuing notes. I am also only too conscious of the infancy of the methodology introduced in these notes. However, it is my sincere hope that exposure to a wider audience will accelerate its maturity. Readers are assumed to be familiar with the basic theory of time series analysis. The book by Professor M.B. Priestley (1981) may be used as a general reference. Chapter One is addressed to the general question: "why do we need non-linear time series models?" After describing some significant advantages of linear models, it singles out several major limitations of linearity. Of course, the selection reflects my personal view on the subject, which is only at its very beginning, although there does seem to be a general agreement in the literature that time irr'eversibility and limit cycles are among the most obvious.
| Author | : David Siegmund |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 1985-08-07 |
| Genre | : Mathematics |
| ISBN | : 9780387961347 |
The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical analysis of many of the proposals and hence to understand them better.
| Author | : K. R. W. Brewer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 173 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1468494074 |
Work for this mono graph on sampling wi th unequal probabili ties was started when Muhammad Hanif was a visitor to the then Commonwealth Bureau of Census and Statistics, Canberra, in 1969. It remained in abeyance until he again visi ted Canberra, this time the Australian National University's Survey Research Centre in 1978 as Visiting Fellow. The work was substantially completed when K.R.W. Brewer visited EI-Fateh University during January 1980 as Visiting Professor. Finally, in 1982 the Bibliography was revised and corrected, and a number of references added which da not appeal" in the text. These are indicated by an asterisk (:, q. The authors are indebted to Mr. E.K. foreman and the sampling staff (past and present) at the Australian Bureau of Statistics for their help and encouragement and tü t-lrs Bar:='ara Geary für her excellent mathematical typing. Canberra K.R.W. Brewer May 1982. Muhammad Hanif vii CONTENTS CHAPTER 1: ..1;1 r:17~ODUCTION TO SAMPLING WITH UNEQUAL PP. OBABILITIES 1 ... Sam.::: Basic Concepts ~j"otation and Abbreviations 4 1
| Author | : R. Gilchrist |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 195 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461257719 |
This volume of Lecture Notes in Statistics consists of the published proceedings of the first international conference to be held on the topic of generalised linear models. This conference was held from 13 - 15 September 1982 at the Polytechnic of North London and marked an important stage in the development and expansion of the GLIM system. The range of the new system, tentatively named Prism, is here outlined by Bob Baker. Further sections of the volume are devoted to more detailed descriptions of the new facilities, including information on the two different numerical methods now available. Most of the data analyses in this volume are carried out using the GLIM system but this is, of course, not necessary. There are other ways of analysing generalised linear models and Peter Green here discusses the many attractive features of APL, including its ability to analyse generalised linear models. Later sections of the volume cover other invited and contributed papers on the theory and application of generalised linear models. Included amongst these is a paper by Murray Aitkin, proposing a unified approach to statistical modelling through direct likelihood inference, and a paper by Daryl Pregibon showing how GLIM can be programmed to carry out score tests. A paper by Joe Whittaker extends the recent discussion of the relationship between conditional independence and log-linear models and John Hinde considers the introduction of an independent random variable into a linear model to allow for unexplained variation in Poisson data.
