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A Comparison of the Bayesian and Frequentist Approaches to Estimation / by Francisco J. Samaniego
(Springer Series in Statistics. ISSN:2197568X)
版 | 1st ed. 2010. |
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出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 2010 |
本文言語 | 英語 |
大きさ | XIII, 225 p : online resource |
著者標目 | *Samaniego, Francisco J author SpringerLink (Online service) |
件 名 | LCSH:Probabilities LCSH:Statistics LCSH:Sociology -- Methodology 全ての件名で検索 FREE:Probability Theory FREE:Statistical Theory and Methods FREE:Sociological Methods |
一般注記 | Point Estimation from a Decision-Theoretic Viewpoint -- An Overview of the Frequentist Approach to Estimation -- An Overview of the Bayesian Approach to Estimation -- The Threshold Problem -- Comparing Bayesian and Frequentist Estimators of a Scalar Parameter -- Conjugacy, Self-Consistency and Bayesian Consensus -- Bayesian vs. Frequentist Shrinkage in Multivariate Normal Problems -- Comparing Bayesian and Frequentist Estimators under Asymmetric Loss -- The Treatment of Nonidentifiable Models -- Improving on Standard Bayesian and Frequentist Estimators -- Combining Data from “Related” Experiments -- Fatherly Advice This monograph contributes to the area of comparative statistical inference. Attention is restricted to the important subfield of statistical estimation. The book is intended for an audience having a solid grounding in probability and statistics at the level of the year-long undergraduate course taken by statistics and mathematics majors. The necessary background on Decision Theory and the frequentist and Bayesian approaches to estimation is presented and carefully discussed in Chapters 1–3. The “threshold problem” -- identifying the boundary between Bayes estimators which tend to outperform standard frequentist estimators and Bayes estimators which don’t -- is formulated in an analytically tractable way in Chapter 4. The formulation includes a specific (decision-theory based) criterion for comparing estimators. The centerpiece of the monograph is Chapter 5 in which, under quite general conditions, an explicit solution to the threshold is obtained for the problem of estimating a scalar parameter under squared error loss. The six chapters that follow address a variety of other contexts in which the threshold problem can be productively treated. Included are treatments of the Bayesian consensus problem, the threshold problem for estimation problems involving of multi-dimensional parameters and/or asymmetric loss, the estimation of nonidentifiable parameters, empirical Bayes methods for combining data from ‘similar’ experiments and linear Bayes methods for combining data from ‘related’ experiments. The final chapter provides an overview of the monograph’s highlights and a discussion of areas and problems in need of further research. F. J. Samaniego is a Distinguished Professor of Statistics at the University of California, Davis. He served as Theory and Methods Editor of the Journal of the American Statistical Association (2003-05), was the 2004 recipient of the Davis Prize for Undergraduate Teaching and Scholarly Achievement, and is an electedFellow of the ASA, the IMS and the RSS and an elected Member of the ISI HTTP:URL=https://doi.org/10.1007/978-1-4419-5941-6 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781441959416 |
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EB00227006 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA273.A1-274.9 DC23:519.2 |
書誌ID | 4000120744 |
ISBN | 9781441959416 |
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