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Title: On the relationships between \alpha-connections and the asymptotic properties of predictive distributions
Author: Corcuera Valverde, José Manuel
Giummolè, F.
Keywords: Distribució (Teoria de la probabilitat)
Anàlisi asimptòtica
Geometria diferencial
Estadística matemàtica
Universitat de Barcelona. Institut de Matemàtica
Issue Date: 1996
Publisher: Universitat de Barcelona
Series/Report no: Mathematics Preprint Series; 210
Abstract: In a recent paper Komaki studies the second-order asymptotic properties of the predictive distributions, using the Kullback-Leibler divergence as loss function. He shows 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 loss function any f-divergence. It appears a relationship between the a-connections and the optimal predictive distributions. In particular, using an a-divergence to measure the goodness of a predictive distribution, the optimal shift of the estimative distribution is related with alpha-covariant derivatives. The expression 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: Preprint enviat per a la seva publicació en una revista científica: Bernoulli, 1999, vol. 5, núm. 1, p. 163-176. []
Note: Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 37.1]
Appears in Collections:Preprints de Matemàtiques - Mathematics Preprint Series

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