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Cramer-Rao bounds for posterior variances

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  • Ghosh, Malay

Abstract

The paper obtains Cramer-Rao type bounds for posterior variances. Conditions are provided for attainability of these bounds. The present bounds are usually more widely applicable, and are often sharper than the ones reported in Schutzenberger (1957). Also, our results extend immediately to find lower bounds of posterior risks, and subsequently of Bayes risks of parameters of interest. Such results can be contrasted to the findings of Gart (1959) who obtained lower bounds for Bayes risks of estimators from which posterior risks are not easy to retrieve. We have provided also multiparameter generalization of our results. Finally, certain Bhattacharyya type bounds for posterior variances are also obtained. In contrast to the usual technique of differentiation under integration for finding Cramer-Rao bounds, our method of proof involves integration by parts.

Suggested Citation

  • Ghosh, Malay, 1993. "Cramer-Rao bounds for posterior variances," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 173-178, June.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:3:p:173-178
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    Cited by:

    1. Pommeret, Denys, 2001. "Posterior variance for quadratic natural exponential families," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 357-362, July.

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