On singularities in linear models with prior information

Abstract

We study the linear model y = X +", given the prior information H =R +v, with three possibilities regarding the knowledge of 2. In each case we obtain the best linear unbiased estimators of , prove its convergence to ˆ and obtain asymptotic relations. This study is also carried out when the design matrix is not of full rank and when the covariance matrix is nonnegative.