Combining Minimax Shrinkage Estimators

Abstract

When one estimates a multivariate normal mean, the use of Stein estimation entails both the grouping of coordinates and the selection of a set of targets toward which to shrink each group. In this article we propose new minimax multiple shrinkage estimators that allow for multiple specifications of these aspects. We provide examples that are evaluated on real and simulated data, including an estimator that adaptively resolves the issue of combining possibly related estimation problems and an adaptive clustering shrinkage estimator. The construction and properties of these estimators are shown to follow from the application of the multiple shrinkage results of George (1986a) to general partitioned shrinkage estimators.

Key Words:

• Bayes estimator
• Mixture
• Multiple shrinkage
• Multivariate normal mean
• Stein estimator
• Superharmonic function
• Unbiased estimate of risk