JSM 2005 - Toronto

Abstract #303742

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Activity Number: 363
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #303742
Title: An Efficient Mixture-based Shrinkage Estimator: A Monte Carlo Analysis
Author(s): William Bolstad*+
Companies: University of Waikato
Address: School of Computing & Math Sciences, Hamilton, not applic, New Zealand
Keywords:
Abstract:

In this paper, we examine the problem of estimating the means of several populations when one or more of the means has been shifted a long way from the others. The shrinkage estimator from the hierarchical normal model would shrink the shifted mean too far from its sample mean, and this would be inefficient. We develop a hierarchical mean model based on a mixture distribution. We perform a Monte Carlo study comparing the efficiencies of the shrinkage estimator based on this model with the shrinkage estimator from the hierarchical normal mean model and a limited translation estimator. We see the mixture shrinkage estimator has good properties. It shrinks all the mean estimates toward the overall mean when none of the means is shifted. When one of the means is shifted a large amount relative to the other means, that estimate is not shifted toward the overall mean very much, and the unshifted means continue to be shrunk toward their overall mean value. The estimator behaves smoothly for shifts between those two extreme cases.

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