Corcuera Valverde, José ManuelGiummolè, Federica2012-04-102012-04-1019991350-7265https://hdl.handle.net/2445/23363In 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.14 p.application/pdfeng(c) ISI/BS, International Statistical Institute, Bernoulli Society, 1999Geometria diferencialConnexions (Matemàtica)Estadística matemàticaTeoria de la prediccióDifferential geometryPrediction theoryConnections (Mathematics)Mathematical statisticsinfo:eu-repo/semantics/article141404info:eu-repo/semantics/openAccess