A1975
Title: On prediction in linear mixed models under misspecified stochastic linear restrictions
Authors: Tatjana von Rosen - Stockholm University (Sweden) [presenting]
Abstract: In many statistical settings, additional (or prior) information about the model parameters is available. Such information can be formulated either as linear exact restrictions, used when a specific linear hypothesis about the parameters is of interest, or as linear stochastic restrictions, used when prior information arises from previous investigations and is subject to uncertainty. A general mixed linear model subject to two competing sets of stochastic linear restrictions, $M_0$ and $M_1$, is considered. The restrictions $M_0$ are assumed to be correct, whereas $M_1$ may be misspecified. Focusing on the best linear unbiased predictors (BLUPs) under mixed models with stochastic restrictions, necessary and sufficient conditions are derived under which the BLUPs obtained under the two competing models coincide. Further conditions are provided under which the BLUP obtained under the model with misspecified restrictions $M_1$ is the BLUP associated with the correct restrictions $M_0$. The approach is based on solving an appropriate system of matrix equations. The same methodology can also be used to study equality of the best linear unbiased estimators of the fixed effects in this context.
