EMPIRICAL BAYES TEST OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

Recently R. S. Singh has studied the empirical Bayes (EB) estimation in a multiple linearregression model. In this paper we consider the EB test of regression coefficient β for this model. Wework out the EB test decision rule by using kernel estimation of multivariate density function and itsfirst order partial derivatives. We obtain its asymptotically optimal (a. o.) property under thecondition E||β||_1<∞. It is shown that tbe convergence rates of this EB test decision rule areO(n^(-(r-1)λ/p+r)) under the condition E||β||^(pr/2-λ)<∞. where an integer r> 0<X<1 and p is the dimensionof the vector.