Convergence rates for empirical bayes estimators of parameters in multi-parameter exponential families

Abstract

This paper obtains the convergence rates of the empirical Bayes estimators of parameters in the multi-parameter exponential families. The rates can approximate to 0(n=¹) arbitrarily. The paper presents the multivariate orthogonal polynomials which are continuous on the total space R^p.

Keywords:

• multi-parameter exponential family
• orthogonal polynomial
• kernel estimation of density
• empirical Bayes
• convergence rate