Utilizing Initial Estimates in Estimating the Coefficients in a Linear Model

A procedure which utilizes an initial estimate to estimate the coefficients in a linear mode is introduced. A linear model containing replications with the same input matrix is considered and a class of two-stage estimators is defined. Optimal estimators in the class are determined, and it is shown that the proposed estimators are better than the corresponding single-sample least squares estimator if the initial estimate is accurate, and are as good (asymptotically) as the corresponding single-sample least squares estimator if the initial estimate is inaccurate.