A Comparison of the Bayesian and Frequentist Approaches to Estimation



Francisco J. Samaniego, "A Comparison of the Bayesian and Frequentist Approaches to Estimation"
Springer | 2010 | ISBN: 1441959408 | 226 pages | File type: PDF | 8,4 mb
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�. 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.

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