Abstract
Samaniego and Reneau presented a landmark study on the comparison of Bayesian and frequentist point estimators. Their findings indicate that Bayesian point estimators work well in more situations than were previously suspected. In particular, their comparison reveals how a Bayesian point estimator can improve upon a frequentist point estimator even in situations where sharp prior knowledge is not necessarily available. In the current paper, we show that similar results hold when comparing Bayesian and frequentist interval estimators. Furthermore, the development of an appropriate interval estimator comparison offers some further insight into the estimation problem.
Highlights
Samaniego and Reneau 1, hereafter referred to as SR, presented a landmark study on the comparison of the Bayesian and frequentist approaches to point estimation
The situation considered for the comparisons in the SR paper, as in the current paper, is relatively simple
Efron 11 writes on the use of indirect information as an important trend in statistics
Summary
Samaniego and Reneau 1 , hereafter referred to as SR, presented a landmark study on the comparison of the Bayesian and frequentist approaches to point estimation. A grander retrospective of the comparison between the Bayesian and frequentist approaches to point estimation is provided in Samaniego 2. We will push the study onward into a comparison of Bayesian and frequentist approaches to the problem of interval estimation. A general theme of Samaniego’s work on comparisons between point estimators. As in the point estimation problem, we show in a comparison of interval estimators that the Bayesian has a generous opportunity for improvement on a frequentist. Samaniego and Neath 6 consider a comparison of estimators in an empirical Bayes framework, leading to the conclusion that the use of prior information, no matter how diffuse, is beneficial. Vestrup and Samaniego 7 compare Bayesian and frequentist shrinkage estimators in a multivariate problem
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