A NOTE ON A BOUND OF THE NORM OF THE DIFFERENCE BETWEEN THE LEAST SQUEARS AND THE BEST LINEAR UNBIASED ESTIMATORS OF THE MEAN VECTOR IN A LINEAR MODEL

Consider the linear model: Y=Xβ+e, where E（e）=0, Cov=σ²V, V is a nonnegative definite matrix. It is well known that μ^*=X（X'X）^-X'Y and \hat\mu=X（X'T^-X）^-X'X^-Y are respectively the least squares and the best linear unbiased estimators of μ=Xβ, where T=V+XUX', U is a symmetric matrix satisfying rank（T）=rank（V:X） and T≥0. In this paper, a bound similar to Haberman’s is obtained when a certain condition is satisfied. If the vector norm involved is taken as the Euclidean one, a set of necessary and suffciant conditions that is easily applicable for Haborman’s condition to be true is obtained. We prove an extended form of a bound similar to that of 2, and also extend bound 3 to that V≥0.