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1999

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/23363

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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Geometria diferencial, Connexions (Matemàtica), Estadística matemàtica, Teoria de la predicció

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Differential geometry, Prediction theory, Connections (Mathematics), Mathematical statistics

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Articles publicats en revistes (Matemàtiques i Informàtica)

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CORCUERA VALVERDE, José Manuel and GIUMMOLÈ, Federica. On the relationship between alpha connections and the asymptotic properties of predictive distributions. Bernoulli. 1999. Vol. 5, num. 1, pags. 163-176. ISSN 1350-7265. [consulted: 12 of October of 2026]. Available at: https://hdl.handle.net/2445/23363

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