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On The Convergence Rates Of Empirical Bayes Rules For Two Action Problems Discrete Case
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Book Synopsis On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case by : Ta Chen Liang
Download or read book On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case written by Ta Chen Liang and published by . This book was released on 1987 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convergence Rates for Empirical Bayes Two-action Problems I. Discrete Case by : STANFORD UNIV CALIF DEPT OF STATISTICS.
Download or read book Convergence Rates for Empirical Bayes Two-action Problems I. Discrete Case written by STANFORD UNIV CALIF DEPT OF STATISTICS. and published by . This book was released on 1967 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Rates of Convergence for Empirical Bayes Two-action Problems: Discrete Case by : TaChen Liang
Download or read book Rates of Convergence for Empirical Bayes Two-action Problems: Discrete Case written by TaChen Liang and published by . This book was released on 1991 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence Rates for Empirical Bayes Two-action Problems II, Continuous Case by : STANFORD UNIV CALIF DEPT OF STATISTICS.
Download or read book Convergence Rates for Empirical Bayes Two-action Problems II, Continuous Case written by STANFORD UNIV CALIF DEPT OF STATISTICS. and published by . This book was released on 1967 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Rates of Convergence in Empirical Bayes Two-action and Estimation Problems and in Extended Sequence-compound Estimation Problems by : Benito Ong Yu
Download or read book Rates of Convergence in Empirical Bayes Two-action and Estimation Problems and in Extended Sequence-compound Estimation Problems written by Benito Ong Yu and published by . This book was released on 1971 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rates of Convergence in Empirical Bayes Decision Problems by : Michael Kelly Mara
Download or read book Rates of Convergence in Empirical Bayes Decision Problems written by Michael Kelly Mara and published by . This book was released on 1975 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Empirical Bayes Two-action Rules with Floating Optimal Sample Size and Exponential Conditional Distributions by : Pekka Laippala
Download or read book The Empirical Bayes Two-action Rules with Floating Optimal Sample Size and Exponential Conditional Distributions written by Pekka Laippala and published by . This book was released on 1980 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Statistical Decision Theory and Applications by : S. Panchapakesan
Download or read book Advances in Statistical Decision Theory and Applications written by S. Panchapakesan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Selected Papers by : Herbert Robbins
Download or read book Selected Papers written by Herbert Robbins and published by Springer. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parametric Empirical Bayes Problems with Cost for Component Observations by : Inna Jung
Download or read book Parametric Empirical Bayes Problems with Cost for Component Observations written by Inna Jung and published by . This book was released on 1988 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Application of a Dominated Convergence Theorem to the Empirical Bayes Problem by : J. J. Deely
Download or read book Application of a Dominated Convergence Theorem to the Empirical Bayes Problem written by J. J. Deely and published by . This book was released on 1974 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to obtain weaker sufficient conditions than those given by Robbins for the asymptotic optimality of empirical Bayes procedures. In so doing a general method for proving asymptotic optimality is given which because of its simplicity should prove quite useful not only for the empirical Bayes problem but for other related asymptotic problems as well. Three areas of application are indicated.
Book Synopsis Bayesian Statistics and Its Applications by : Satyanshu K. Upadhyay
Download or read book Bayesian Statistics and Its Applications written by Satyanshu K. Upadhyay and published by Anshan Pub. This book was released on 2007 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Technical Reports Awareness Circular : TRAC. by :
Download or read book Technical Reports Awareness Circular : TRAC. written by and published by . This book was released on 1987-08 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Chinese Journal of Contemporary Mathematics by :
Download or read book Chinese Journal of Contemporary Mathematics written by and published by . This book was released on 1999 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Theory and Method Abstracts by :
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 1989 with total page 1092 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parametric Statistical Inference by : Shelemyahu Zacks
Download or read book Parametric Statistical Inference written by Shelemyahu Zacks and published by Elsevier. This book was released on 2014-05-20 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parametric Statistical Inference: Basic Theory and Modern Approaches presents the developments and modern trends in statistical inference to students who do not have advanced mathematical and statistical preparation. The topics discussed in the book are basic and common to many fields of statistical inference and thus serve as a jumping board for in-depth study. The book is organized into eight chapters. Chapter 1 provides an overview of how the theory of statistical inference is presented in subsequent chapters. Chapter 2 briefly discusses statistical distributions and their properties. Chapter 3 is devoted to the problem of sufficient statistics and the information in samples, and Chapter 4 presents some basic results from the theory of testing statistical hypothesis. In Chapter 5, the classical theory of estimation is developed. Chapter 6 discusses the efficiency of estimators and some large sample properties, while Chapter 7 studies the topics on confidence intervals. Finally, Chapter 8 is about decision theoretic and Bayesian approach in testing and estimation. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability will highly benefit from this book.
Download or read book Naval Research Reviews written by and published by . This book was released on 1968 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
