Semiparametrics, Nonparametrics and Empirical Bayes Procedures in Linear Models

In a classical parametric setup, a key factor in the implementation of the Empirical Bayes methodology is the incorporation of a suitable prior that is compatible with the parametric setup and yet lends to the estimation of the Bayes (shrinkage) factor in an empirical manner. The situation is more complex in semi-parametric and (ev,:,n more in) nonparametric models. Although the Dirichlet priors have been considered in some simple non parametric models, in a general linear model there are certain limitations for such procedures, and alternative semiparametric methods have gained popularity in practice. Using first-order asymptotic representations for semiparametric and nonparametric estimators it is shown that a general Gaussian prior on the regression parameters can be readily adopted to formulate suitable empirical Bayes estimators that are essentially related to robust Stein-rule versions of such estimators which were introduced in the statistical lierature in a somewhat different perspective. Properties of such robust empirical Bayes estimators are studied.