Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 1, pp. 128--134

SECOND ORDER ADMISSIBILITY OF GENERALIZED BAYES ESTIMATOR UNDER JEFFREYS' PRIOR

By

YOSHIJI TAKAGI, Osaka Prefecture University, Sakai

SUMMARY. It is shown that a parametrization-invariant second order estimator is asymptotically equivalent to the generalized Bayes estimator under Jeffreys' prior, up to the order Op(1/n). This result suggests that Jeffreys' prior should be chosen as a desirable prior for the determination of noninformative priors by a formal rule.

AMS (1991) subject classification. 62C10, 62C15, 62F12.

Key words and phrases. Second order admissibility, parametrization invariance, Jeffreys' prior, generalized Bayes estimator.

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