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.
"A Bound for the Euclidean Norm of the Difference Between the Least Squares and the Best Linear Unbiased Estimators." Ann. Statist. 6 (6) 1390 - 1393, November, 1978. https://doi.org/10.1214/aos/1176344383