A comparison of the Bayesian and frequentist approaches to estimation
By: Francisco J. Samaniego
Series: Springer series in statistics; Springer series in statistics
Publisher: Springer
Published: 2010
Place of publication: New York; London
Language: eng
Number of pages: 225
ISBN-13: 9781441959409
Subjects: Bayesian statistical decision theory; Mathematical statistics; Estimation theory; Statistical decision
Description: "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 multidimensional 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."--BOOK JACKET.
Notes: Includes bibliographical references (p. [213]-219) and index.