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
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.
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