On The Convergence Rates Of Empirical Bayes Rules For Two Action Problems Discrete Case PDF Download
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Author | : Ta Chen Liang |
Publisher | : |
Total Pages | : 16 |
Release | : 1987 |
Genre | : |
ISBN | : |
Download On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case Book in PDF, ePub and Kindle
The purpose of this paper is to investigate the convergence rates of a sequence of empirical Bayes decision rules for the two-action decision problems where the distributions of the observations belong to a discrete exponential family. It is found that the sequence of the empirical Bayes decision rules under study is asymptotically optimal, and the order of associated convergence rates is O(exp( -cn)), for some positive constant c, where n is the number of accumulated past experience (observations) at hand. Two examples are provided to illustrate the performance of the proposed empirical Bayes decision rules. A comparison is also made between the proposed empirical Bayes rules and some earlier existng empirical Bayes rules.
Author | : STANFORD UNIV CALIF DEPT OF STATISTICS. |
Publisher | : |
Total Pages | : 41 |
Release | : 1967 |
Genre | : |
ISBN | : |
Download Convergence Rates for Empirical Bayes Two-action Problems I. Discrete Case Book in PDF, ePub and Kindle
A sequence of decision problems is considered where for each problem the observation has discrete probability function of the form p(x) = h(x) beta (lambda) lambda to the power x, x = 0,1,2, ..., and where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that for each problem one of two possible actions (e.g., 'accept' or 'reject') must be selected. Under various assumptions about h(x) and G(lambda) the rate at which the risk of the nth problem approaches the smallest possible risk is determined for standard empirical Bayes procedures. It is shown that for most practical situations, the rate of convergence to 'optimality' will be at least as fast as L(n)/n where L(n) is a slowly varying function (e.g., log n). The rate cannot be faster than 1/n and this exact rate is achieved in some cases. Arbitrarily slow rates will occur in certain pathological situations. (Author).
Author | : TaChen Liang |
Publisher | : |
Total Pages | : 12 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download Rates of Convergence for Empirical Bayes Two-action Problems: Discrete Case Book in PDF, ePub and Kindle
Author | : STANFORD UNIV CALIF DEPT OF STATISTICS. |
Publisher | : |
Total Pages | : 28 |
Release | : 1967 |
Genre | : |
ISBN | : |
Download Convergence Rates for Empirical Bayes Two-action Problems II, Continuous Case Book in PDF, ePub and Kindle
A sequence of decision problems is considered where for each problem the observation has a probability density function of exponential type with parameter lambda where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that in each of the problems, one of two possible actions (e.g., 'accept' or 'reject') must be taken. Under various assumptions, reasonably sharp upper bounds are found for the rate at which the risk of the nth problem approaches the smallest possible risk for certain refinements of the standard empirical Bayes procedures. For suitably chosen procedures, under situations likely to occur in practice, rates faster than n to the power ( -1 + epsilon) may be obtained for arbitrarily small epsilon> 0. Arbitrarily slow rates can occur in pathological situations. (Author).
Author | : Pekka Laippala |
Publisher | : |
Total Pages | : 92 |
Release | : 1980 |
Genre | : Bayesian statistical decision theory |
ISBN | : |
Download The Empirical Bayes Two-action Rules with Floating Optimal Sample Size and Exponential Conditional Distributions Book in PDF, ePub and Kindle
Author | : Benito Ong Yu |
Publisher | : |
Total Pages | : 126 |
Release | : 1971 |
Genre | : Bayesian statistical decision theory |
ISBN | : |
Download Rates of Convergence in Empirical Bayes Two-action and Estimation Problems and in Extended Sequence-compound Estimation Problems Book in PDF, ePub and Kindle
Author | : Herbert Robbins |
Publisher | : Springer |
Total Pages | : 530 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461251109 |
Download Selected Papers Book in PDF, ePub and Kindle
Herbert Robbins is widely recognized as one of the most creative and original mathematical statisticians of our time. The purpose of this book is to reprint, on the occasion of his seventieth birthday, some of his most outstanding research. In making selections for reprinting we have tried to keep in mind three potential audiences: (1) the historian who would like to know Robbins' seminal role in stimulating a substantial proportion of current research in mathematical statistics; (2) the novice who would like a readable, conceptually oriented introduction to these subjects; and (3) the expert who would like to have useful reference material in a single collection. In many cases the needs of the first two groups can be met simulta neously. A distinguishing feature of Robbins' research is its daring originality, which literally creates new specialties for subsequent generations of statisticians to explore. Often these seminal papers are also models of exposition serving to introduce the reader, in the simplest possible context, to ideas that are important for contemporary research in the field. An example is the paper of Robbins and Monro which initiated the subject of stochastic approximation. We have also attempted to provide some useful guidance to the literature in various subjects by supplying additional references, particularly to books and survey articles, with some remarks about important developments in these areas.
Author | : S. Panchapakesan |
Publisher | : Springer Science & Business Media |
Total Pages | : 478 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461223083 |
Download Advances in Statistical Decision Theory and Applications Book in PDF, ePub and Kindle
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 | : Inna Jung |
Publisher | : |
Total Pages | : 110 |
Release | : 1988 |
Genre | : Bayesian statistical decision theory |
ISBN | : |
Download Parametric Empirical Bayes Problems with Cost for Component Observations Book in PDF, ePub and Kindle
Author | : Satyanshu K. Upadhyay |
Publisher | : Anshan Pub |
Total Pages | : 528 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : |
Download Bayesian Statistics and Its Applications Book in PDF, ePub and Kindle
In the last two decades, Bayesian Statistics has acquired immense importance and has penetrated almost every area including those where the application of statistics appeared to be a remote possibility. This volume provides both theoretical and practical insights into the subject with detailed up-to-date material on various aspects. It serves two important objectives - to offer a thorough background material for theoreticians and gives a variety of applications for applied statisticians and practitioners. Consisting of 33 chapters, it covers topics on biostatistics, econometrics, reliability, image analysis, Bayesian computation, neural networks, prior elicitation, objective Bayesian methodologies, role of randomisation in Bayesian analysis, spatial data analysis, nonparametrics and a lot more. The book will serve as an excellent reference work for updating knowledge and for developing new methodologies in a wide variety of areas. It will become an invaluable tool for statisticians and the practitioners of Bayesian paradigm.