Optimal Shrinkage Estimation in Heteroscedastic Hierarchical Models: Beyond Gaussian

• Activity Number: 583
• Type: Invited
• Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Samuel Kou* and Lawrence D. Brown and Xianchao Xie
• Companies: Harvard and University of Pennsylvania and Two Sigma Investments
• Keywords: quadratic variance function ; exponential family ; location-scale family ; linear regression ; hierarchical linear model ; asymptotic optimality

Abstract

Hierarchical models are powerful statistical tools widely used in scientific and engineering applications. The homoscedastic (equal variance) case has been extensively studied, and it is well known that shrinkage estimates, the James-Stein estimate in particular, offer nice theoretical (e.g., risk) properties. The heteroscedastic (the unequal variance) case, on the other hand, has received less attention, even though it frequently appears in real applications. It is not clear of how to construct "optimal" shrinkage estimate. In this talk, we study this problem. In particular, we consider models beyond Gaussian. We introduce a class of shrinkage estimates, constructed by minimizing an unbiased risk statistic. We will show that this class is asymptotically optimal in the heteroscedastic case. We apply the estimates to real examples and observe competitive numerical results.