A1979
Title: Bayes linear estimator in the general linear model
Authors: Hirai Mukasa - Kyushu University (Japan) [presenting]
Abstract: The Bayes linear estimator is derived by minimizing the Bayes risk with respect to squared loss in the general linear model. When certain prior information is available, it is often natural to consider Bayes linear estimators. For example, generalized least squares, ridge, and shrinkage estimators can be represented as Bayes linear estimators or limit points thereof. Statistical properties and equivalence of Bayes linear estimators are discussed. First, properties of Bayes linear estimators such as linear sufficiency and linear completeness are explored. These properties are important concepts that characterize whether a linear estimator retains sufficient and nonredundant information to construct the best linear unbiased estimator for a linear predictor. Second, necessary and sufficient conditions under which two Bayes linear estimators coincide are derived. These conditions clarify when different choices of covariance structures or prior information lead to the same estimator. As an illustration, linear mixed-effects models are considered and results are shown to provide a more efficient estimation procedure.
