Abstract: By using kernel estimators of a multivariate density function and its partial derivatives, and the estimators of the nuisance parameters, we construct empirical Bayes (EB) estimators of parameters in a class of linear models. Under suitable moment conditions on the prior distribution, the proposed EB estimators are asymptotically optimal with rates arbitrarily close to o(n-1).
Key words and phrases: Convergence rates, empirical Bayesian estimation, linear models.