## The Annals of Statistics

### Mean squared error of empirical predictor

#### 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.

#### Article information

Source
Ann. Statist., Volume 32, Number 2 (2004), 818-840.

Dates
First available in Project Euclid: 28 April 2004

https://projecteuclid.org/euclid.aos/1083178948

Digital Object Identifier
doi:10.1214/009053604000000201

Mathematical Reviews number (MathSciNet)
MR2060179

Zentralblatt MATH identifier
1092.62063

#### Citation

Das, Kalyan; Jiang, Jiming; Rao, J. N. K. Mean squared error of empirical predictor. Ann. Statist. 32 (2004), no. 2, 818--840. doi:10.1214/009053604000000201. https://projecteuclid.org/euclid.aos/1083178948

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