A comparison of the Bayesian and frequentist approaches to estimation
type: Item
instance of: scholarly article
title: A comparison of the Bayesian and frequentist approaches to estimation
zbMATH Open document ID: 1204.62028
DOI: 10.1007/978-1-4419-5941-6
author: Francisco J. Samaniego
published in: Springer Series in Statistics
publication date: 2010-08-11T00:00:00Z
review text: The book under review is addressed to the audience of academics and practitioners who are open to using either frequentist or Bayesian methods in the considered problems, but would like to have a defensible basis for using one or the other. It will be appropriate as a text either for an advanced undergraduate course or for a graduate-level course or seminar. The book consists of 12 chapters and an appendix. The first three chapters present a review of decision-theoretic concepts and the basic tools and ideas of frequentist and Bayesian estimation. Then the author proceeds with the comparison of frequentist and Bayesian estimators in a variety of statistical contexts. The ``threshold problem'' is introduced in Chapter 4. It is the problem of identifying the boundary between the circumstances in which Bayes estimators tend to outperform frequentist ones and the complimentary circumstances in which the opposite is true. A criterion for comparing Bayes and frequentist estimators is then formulated. One-parameter problems estimated under squared error loss are considered in Chapter 5, and an explicit solution to the threshold problem, applicable to exponential families of sampling distributions and conjugate families of prior distributions, is given. In Chapter 6, the notion of conjugacy is further explored, both in the light of the concept of Bayesian self-consistency and as a tool for treating the Bayesian consensus problem. In Chapter 7, a multivariate version of the threshold problem is developed for comparing Bayesian and frequentist shrinkage. Generalizations of the threshold problem to estimation under an asymmetric loss function are considered in Chapter 8. In Chapter 9, the efficiency of Bayesian estimators of nonidentifiable parameters is examined through a concrete example in which a fully Bayesian version of the threshold problem is treated for a nonidentifiable binomial model. Nonparametric estimation in the context of competing risks and the estimation of t…
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62A99
zbMATH DE Number: 5768441
reviewed by: Joseph Melamed
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4419-5941-6
OpenAlex ID: W616902621
description: scientific article; zbMATH DE number 5768441