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URL: http://kluedo.ub.uni-kl.de/volltexte/2000/775/
Scholl, Holger
Shannon-Optimal Priors on iid Statistical Experiments Converge Weakly to Jeffreys Prior
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Kurzfassung in englisch
In 1979, J.M. Bernardo argued heuristically that in the case of regular product experiments his information theoretic reference prior is equal to Jeffreys' prior. In this context, B.S. Clarke and A.R. Barron showed in 1994, that in the same class of experiments Jeffreys' prior is asymptotically optimal in the sense of Shannon, or, in Bayesian terms, Jeffreys' prior is asymptotically least favorable under Kullback Leibler risk. In the present paper, we prove, based on Clarke and Barron's results, that every sequence of Shannon optimal priors on a sequence of regular iid product experiments converges weakly to Jeffreys' prior. This means that for increasing sample size Kullback Leibler least favorable priors tend to Jeffreys' prior.
| Freie Schlagwörter (englisch): |
| Jeffreys' prior , Shannon optimal priors , Kullback Leibler distance , noninformative prior , reference prior , minimax risk , Bayes risk |
| Reihe: |
| Sonstige
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| DDC-Sachgruppe: |
| Mathematik |
| Dokumentart: |
| Preprint (Vorabdruck) |
| Sprache: |
| englisch |
| Erstellungsjahr: |
| 1999 |
| Publikationsdatum: |
| 03.04.2000 |
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