Accounting for the estimation of variances and covariances in prediction under a general linear model: an overview

Rok, strany: 2008, 1 - 15

The problem considered is essentially that of predicting a linear combination of the fixed and/or random effects of a linear mixed-effects model. Applications are widespread; they include small-area estimation, the estimation (or prediction) of breeding values, the estimation of treatment contrasts (from the results of a comparative experiment), and the analysis of longitudinal data. The best linear unbiased predictor (BLUP) depends on functions of variance components and/or other such parameters. In practice, the values of these functions are typically unknown, and resort is made to the predictor (the so-called empirical BLUP) obtained from the BLUP by replacing the ``true'' values of the functions with even translation-invariant estimators (such as the REML estimators). This paper provides an overview of various results on the empirical BLUP (and includes a few extensions). The focus is on the mean squared error (MSE) of the empirical BLUP and on the approximation and estimation of the MSE. Some attention is given to prediction intervals.

ISO 690:

Harville, D. 2008. Accounting for the estimation of variances and covariances in prediction under a general linear model: an overview. In Tatra Mountains Mathematical Publications, vol. 39, no.1, pp. 1-15. 1210-3195.

APA:

Harville, D. (2008). Accounting for the estimation of variances and covariances in prediction under a general linear model: an overview. Tatra Mountains Mathematical Publications, 39(1), 1-15. 1210-3195.