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Mean squared error of empirical predictor
K DAS, J JIANG
Published in INST MATHEMATICAL STATISTICS
2004
Volume: 32
   
Issue: 2
Pages: 818 - 840
Abstract
The term "empirical predictor" refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases. © Institute of Mathematical Statistics, 2004.
About the journal
JournalAnnals of Statistics
PublisherINST MATHEMATICAL STATISTICS
ISSN0090-5364
Open AccessYes