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Title: On the relationship between alpha connections and the asymptotic properties of predictive distributions
Author: Corcuera Valverde, José Manuel
Giummolè, Federica
Keywords: Geometria diferencial
Connexions (Matemàtica)
Estadística matemàtica
Teoria de la predicció
Differential geometry
Prediction theory
Connections (Mathematics)
Mathematical statistics
Issue Date: 1999
Publisher: Bernoulli Society for Mathematical Statistics and Probability
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 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.
Note: Reproducció del document publicat a:
It is part of: Bernoulli, 1999, vol. 5, núm. 1, p. 163-176
ISSN: 1350-7265
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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