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April 2004 Mean squared error of empirical predictor
Kalyan Das, Jiming Jiang, J. N. K. Rao
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Ann. Statist. 32(2): 818-840 (April 2004). DOI: 10.1214/009053604000000201


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.


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Kalyan Das. Jiming Jiang. J. N. K. Rao. "Mean squared error of empirical predictor." Ann. Statist. 32 (2) 818 - 840, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1092.62063
MathSciNet: MR2060179
Digital Object Identifier: 10.1214/009053604000000201

Primary: 62F12 , 62J99

Keywords: ANOVA model , EBLUP , longitudinal model , mixed linear model , variance components

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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