On biased linear estimators in models with arbitrary rank

Abstract

In this paper we define a class of biased linear estimators for the unknown parameters in linear models with arbitrary rank. The feature of our approach is to reduce the estimation problem in arbitrary rank models to the one in full-rank models. Some important properties are discussed. As special cases of our class, we extend to deficient-rank models six known biased linear estimators.

Keywords:

• biased estimator
• Bayes linear estimator
• generalized inverse matrix
• mean square error
• prior distribution
• Bayes risk