(Received January 17, 1994; revised July 27, 1994)
Abstract. Empirical Bayes (EB) estimation of the parameter vector theta=(beta', sigma2)' in a multiple linear regression model Y = Xbeta+epsilon is considered, where beta is the vector of regression coefficient, epsilon ~ N(0,sigma2I) and sigma2 is unknown. In this paper, we have constructed the EB estimators of theta by using the kernel estimation of multivariate density function and its partial derivatives. Under suitable conditions it is shown that the convergence rates of the EB estimators are O(n-(lambda k-1)(k-2)/k(2k+p+1)), where the natural number k > 3, 1/3 < lambda < 1, and p is the dimension of vector beta.
Key words and phrases: Empirical Bayes estimation, multiple linear regression model, convergence rates.
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