The Convergence Rate of Simultaneous Empirical Bayes Estimator for Parameters in Linear Regression Models

Abstract:

      In this paper, the simultaneous empirical Bayes (EB) estimator for regression cofficient β= (β₁,…,β_p)′ and error variance σ² is considered in linear models. Suppose that the loss function is square, the convergence rate of simultaneous EB estimator about the parameter θ=(β₁,…,β_p,σ²) is obtained and this convergence rate can be arbitrarily close to 1 under suitable conditions. At last, an example is given.