Observed Best Prediction via Nested-Error Regression

• Activity Number: 635
• Type: Invited
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: WNAR
• Author(s): Jiming Jiang*+ and Thuan Nguyen and J.S. Rao
• Companies: University of California at Davis and Oregon Health and Science University and University of Miami
• Keywords: area-specific MSPE ; design-unbiasedness ; heteroscedasticity ; ID ; model misspecification ; small area estimation

Abstract

We consider the observed best prediction (OBP; Jiang, Nguyen & Rao 2011) for small area estimation under the nested-error regression model (NER; Battese et al. 1988), where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. We propose an estimator of the area-specific MSPE of the OBP that is asymptotically nonnegative and is second-order unbiased in an overall sense. The latter is reasonable due to the potential model misspecifications. We introduce a method for obtaining functional expressions, call indirect derivation (ID), that avoids tedious derivations. The ID method is used to derive the proposed MSPE estimatorr, and it is potentially useful in solving other problems as well. We evaluate performance of the proposed MSPE estimator through a simulation study. A real data example is considered.