Robust Minimax Shrinkage Estimation for Spherically Symmetric Distributions Under Concave Loss

• Activity Number: 540
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): William E. Strawderman*+
• Companies: Rutgers University

Abstract

Improved Stein-type estimators are proposed for the k- dimensional mean vector in the case of spherically symmetric distributions with residual vectors under loss functions that are concave functions of squared error. It is shown that certain Stein-type shrinkage estimators have the strong robustness property that they beat the standard unbiased estimator simultaneously for all spherically symmetric distributions (with a finite second moment), uniformly for a wide class of concave losses. As an example, the James-Stein Estimator (with estimated scale parameter) dominates the usual estimator simultaneously for all Lp loss functions (truncated or untruncated) and all spherically symmetric distributions when the dimension k, is greater than or equal to 5 and the shrinkage constant is less than or equal to (k-4)/k times the maximum possible constant for usual squared error loss.