A note on the convergence rates for empirical bayes estimators of parameters in multiple-parameter exponential families

Abstract

Under suitable conditions upon prior distribution, the convergence rates for empirical Bayes estimators of parameters in multi-parameter exponential families (M-PEF) are obtained. It is shown that the assumptions Tong (1996) imposed on the marginal density can be reduced. The above result can also be extended to more general forms of M-PEF. Finally, some examples which satisfy the conditions of the theorems are given.

Keywords:

• a note
• multi-parameter exponential family
• kernel estimation
• empirical Bayes estimation
• convergence rates