Integral Inequality for Minimaxity and Characterization of Priors by Use of Inverse Laplace Transform

Tatsuya Kubokawa
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Tatsuya Kubokawa: Faculty of Economics, University of Tokyo

No CIRJE-F-393, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a differential inequality studied in the literature, but also handles non-differentiable or discontinuous estimators. The paper also gives characterization of prior distributions such that the resulting Bayes equivariant or generalized Bayes estimators are minimax. This characterization is provided by using the inverse Laplace transform. Finally, a simple proof for constructing a class of estimators improving on the James-Stein estimator is given based on the integral expression of the risk.

Pages: 33 pages
Date: 2006-01
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2006cf393

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