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February 1999 On the relationship between α connections and the asymptotic properties of predictive distributions
José M. Corcuera, Federica Giummolè
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Bernoulli 5(1): 163-176 (February 1999).

Abstract

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between α connections and optimal predictive distributions. In particular, using an α divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to α-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Citation

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José M. Corcuera. Federica Giummolè. "On the relationship between α connections and the asymptotic properties of predictive distributions." Bernoulli 5 (1) 163 - 176, February 1999.

Information

Published: February 1999
First available in Project Euclid: 12 March 2007

zbMATH: 0916.62014
MathSciNet: MR1673576

Keywords: curved exponential family , Differential geometry , f divergences , predictive distributions , second-order asymptotic theory , α connections , α embedding curvature

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

Vol.5 • No. 1 • February 1999
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