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

Abstract

Haberman's bound for a norm of the difference between the least squares and the best linear unbiased estimators in a linear model with nonsingular covariance structure is examined in the particular case when a vector norm involved is taken as the Euclidean one. In this frequently occurring case, a new substantially improved bound is developed which, furthermore, is applicable regardless of any additional condition.