A New Bound for the Euclidean Norm of the Difference Between the Least Squares and the Best Linear Unbiased Estimators

Abstract

A new bound is established for the Euclidean norm of the difference between the least squares estimator and the best linear unbiased estimator of the vector of expectations in the general linear model. The bound is valid regardless of the rank of the dispersion matrix and is expressed in substantially simpler terms than the bounds given earlier by Haberman and by Baksalary and Kala.