Majumdar (1994, J. Multivariate Anal.48 87-105) compounds (in the sense of Robbins, 1951, "Proceedings, Second Berkeley Sympos. Math. Statist. Probab.," pp. 131-148, Univ. of California Press, Berkeley) the estimation problem in the mean-parameter family of Gaussian distributions on a real separable infinite dimensional Hilbert space. The question of asymptotic optimality of compound estimators that are Bayes versus a hyperprior mixture of i.i.d. priors on the compound parameter is reduced there, under a compactness restriction on the parameter space, to the question of consistency, in an extended sense, of a certain posterior mixture for the empirical mixture. For mixing hyperpriors with full topological support, that consistency result is obtained in this paper. A corollary of the consistency result is applied to obtain asymptotically optimal decision rules in the empirical Bayes problem involving the mean-parameter Gaussian family and a sufficiently smooth risk function.
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Volume (Year): 55 (1995) Issue (Month): 2 (November) Pages: 187-204 Download reference. The following formats are available: HTML
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