Abstract: In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are O(n^{-2(kλ-1)/(2k+m)}) under the condition ∫_Θ||β||^{((m+ξ)λ/η-λ)V(2kλ)}dG<∞.where an integer k > 1.1/2 < λ < η < 1.ξ > 0 is an arbitrary small number and m is the dimension of the vector Y.

Key words: Linear regression model, estimable function, empirical Bayes estimation, convergence rates