A1053
Title: On the invariance of the best linear unbiased estimators under the partitioned linear model
Authors: Tatjana von Rosen - Stockholm University (Sweden) [presenting]
Abstract: A linear model with two sets of covariates is considered. Splitting covariates into two sets is often motivated by their nature, for example, patient-related and disease-related covariates. Depending on the nature of the covariates in the set, a partitioned fixed effects model or the mixed effects model can be formulated. The focus is on the estimation of fixed effects in one set of covariates being of primary interest. In particular, the necessary and sufficient conditions for the best linear unbiased estimator to be invariant with respect to the nature of the covariates in the other set will be derived. The proposed approach to establishing these conditions is based on solving a certain system of matrix equations. The consistency of the system of matrix equations is equivalent to the existence of the invariant BLUEs. Finally, the obtained conditions will be related to the existing ones often expressed using the linear spaces approach, for example, via column spaces of concern matrices.
