Multivariate Generalized Stein Estimate and Its Optimality Cai Xinmin Fang Xing Huang Yangxin School of Science,WUT,Wuhan 430070,China.For multivariate normal linear model, a nonlinear biased estimate of regression coefficients, which is multivariate generalized Stein estimate, is presented by the method of minimizing mean square error of linear estimate in this paper. Its asymptotic expansions of bias and mean square error are derived, and when error disturbance is sufficiently small, the asymptotic necessary and sufficient conditions are also shown for this estimate to dominate the best linear unbiased estimate under the mean square error criterion.multivariate linear model; mean square error; multivariate generalized Stein estimate; least squares estimate; asymptotic property