Title:
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On the relationship between connections and the asymptotic properties of predictive distributions
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Author:
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Corcuera Valverde, José Manuel; Giummolè, Federica
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Other authors:
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Universitat de Barcelona |
Abstract:
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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. |
Subject(s):
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-Geometria diferencial -Connexions (Matemàtica) -Estadística matemàtica -Teoria de la predicció -Differential geometry -Prediction theory -Connections (Mathematics) -Mathematical statistics |
Rights:
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(c) ISI/BS, International Statistical Institute, Bernoulli Society, 1999
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Document type:
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Article Article - Published version |
Published by:
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Bernoulli Society for Mathematical Statistics and Probability
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