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On the relationship between alpha connections and the asymptotic properties of predictive distributions

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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 alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-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.

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Bernoulli Society for Mathematical Statistics and Probability

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(c) ISI/BS, International Statistical Institute, Bernoulli Society, 1999

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On the relationship between alpha connections and the asymptotic properties of predictive distributions