JSM 2005 - Toronto

Abstract #302421

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 166
Type: Invited
Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #302421
Title: High-dimensional Predictive Estimation
Author(s): Edward I. George*+ and Lawrence Brown and Feng Liang and Xinyi Xu
Companies: University of Pennsylvania and University of Pennsylvania and Duke University and University of Pennsylvania
Address: 3730 Walnut St, 400 JMHH, Philadelphia, PA, 19104,
Keywords: admissibility ; Bayes rules ; decision theory ; minimaxity ; shrinkage estimation ; superharmonic priors
Abstract:

Let X and Y be independent p-dimensional multivariate normal vectors with common unknown mean. Based only on observing X = x, we will consider the problem of estimating the entire predictive distribution of Y under expected Kullback-Leibler loss. We will show the natural straw man for this decision problem is dominated by any Bayes rule for which the square root of the marginal distribution is superharmonic, which includes Bayes rules under superharmonic priors. We further will show that Bayes rules form a complete class for this problem and give sufficient conditions for admissibility. Finally, these results will be seen to extend naturally to predictive estimation under the normal linear regression model. Fundamental similarities and differences with the parallel theory of estimating a multivariate normal mean under quadratic loss will be described throughout.

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