Some Results in Finding A Lower Bound of the Efficiency of Least Square Estimates Relative to Best Linear Estimates in Regression Model

Consider the usual regression model Y = X + . The standard estimators of  are (i) Least squares estimator and (ii) Best linear estimator. The paper gives some results on finding an attainable lower bound on the efficiency of least square estimates relative to the best linear estimate. Specifically the paper is an attempt to verify the validity of a conjecture made by G.S. Watson.