Best Predictive Estimation in Linear Mixed Models

• Activity Number: 1
• Type: Invited
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): J. Sunil Rao*+ and Jiming Jiang and Thuan Nguyen
• Companies: University of Miami and University of California at Davis and Oregon Health & Science University
• Keywords: mixed models ; best predictive estimator ; model misspecification

Abstract

We start by deriving the best predictive estimator (BPE) of the fixed parameters under a well-known linear mixed model, the Fay-Herriot model. This leads to a new prediction procedure, called observed best prediction (OBP), which is different from the empirical best linear unbiased prediction (EBLUP). We show that BPE is more reasonable than the traditional estimators derived from estimation considerations, such as maximum likelihood (ML) and restricted maximum likelihood (REML), if the main interest is estimation of the mixed effect, which is a mixed model prediction problem. We use both theoretical derivations and empirical studies to demonstrate that the OBP can significantly outperform EBLUP, if the underlying model is misspecified. On the other hand, when the underlying model is correctly specified, the predictive performance of the OBP is very similar to that of the EBLUP. A general theory for OBP in the context of mixed model prediction is developed next, and a real data example is considered.

This is joint work with Jiming Jiang of UC-Davis and Thuan Nguyen of Oregon Health and Science University.