Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 106--117

EMPIRICAL BAYES ESTIMATION IN A THRESHOLD MODEL

By

SOMNATH DATTA, University of Georgia

SUMMARY. Empirical Bayes estimation in a general threshold model is considered. Assuming a bounded parameter space, we obtain a uniform (w.r.t. the unknown prior distribution) and non-asymptotic upper bound on the regret of a class of empirical Bayes estimators corresponding to different kernels and bandwidths. The optimal choice of the bandwidth gives an asymptotically optimal solution in the sense of Robbins with O(n1/2) rate.

In addition to the upper bounds, an asymptotic lower bound for the regret of our empirical Bayes estimators is also derived. The asymptotic order of lower bound for the optimal bandwidth turns out to be the same as that of the upper bound.

AMS (1990) subject classification. Primary 62C12; secondary 62F10.

Key words and phrases. Empirical Bayes estimation, nonexponential family, threshold model, squared error loss, asymptotic optimality, rate of convergence.

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