Asymptotic efficiency of estimators of a multivariate linear functional relation1

Abstract

We consider the problem of estimating the parameter T in a multivariate linear functional relation when the errors are independently distributed as with known ∑, and the parameters xi are unknown. The problem of asymptotic efficiency of the maximum likelihood estimator of T is investigated in view of the fact that due to the presence of infinitely many incidental (nuisance) parameters xi, familiar efficiency statements with respect to the m.l.e. fail to be valid. An appropriate theory of asymptotic efficiency is presented, based on a certain model-specific class of estimators. It represents an analogue to the' Gauss-Markov theory of linear estimation in the linear regression model. As a by-product simple asymptotically efficient estimators are obtained.