Comparison of MINQUE and simple estimator of the error variance in the gaussmark off model

Abstract EN

The problem of estimation of variance components occurs in many areas of research.

This paper is devoted to study the comparison between Minimum Norm Quadratic Unbiased Estimator (MINQUE) and Ordinary Least Square Estimator (OLSE) of s 2 in the Gauss Markoff Model {Y, Xb, s 2V}, under mean square errors criterion, where the model matrix X need not have full rank and the dispersion matrix V can be singular.

A necessary and sufficient condition is obtained for that MINQUE is superior to simple estimator, in particular, a simple sufficient condition is that the degree of freedom of errors is equal to or greater than 4.