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Activity Number: 506
Type: Contributed
Date/Time: Thursday, August 10, 2006 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #306794
Title: Robust Prior Bayes Estimation on Infinite Dimensional Normal Mean and Spectral Densities
Author(s): Herman Rubin*+ and Hui Xu
Companies: Purdue University and Purdue University
Address: Department of Statistics, West Lafayette, IN, 47907,
Keywords: prior Bayes robustness ; empirical Bayes ; Bayes risk ; nonparametric estimation
Abstract:

We consider the infinite dimensional normal mean problem from the prior Bayes robustness viewpoint. Assumptions are made that the prior variances are decreasing, with some extensions. Under squared error loss, empirical Bayes estimation of the mean vector is derived without knowing the posterior. The effects of various types of decreasing rates are investigated. It is shown that although we cannot estimate the individual prior parameters consistently, the overall risk of using this kind of estimate is still asymptotically optimal compared to the true prior Bayes risk. Similar methods applies to spectral density estimation.

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