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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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CORCUERA VALVERDE, José manuel, GIUMMOLÈ, Federica. On the relationship between alpha connections and the asymptotic properties of predictive distributions. _Bernoulli_. 1999. Vol. 5, núm. 1, pàgs. 163-176. [consulta: 24 de gener de 2026]. ISSN: 1350-7265. [Disponible a: https://hdl.handle.net/2445/23363]