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Entropy 2014, 16(6), 3026-3048; doi:10.3390/e16063026
Article

Asymptotically Constant-Risk Predictive Densities When the Distributions of Data and Target Variables Are Different

1,*  and 1,2
Received: 28 March 2014 / Revised: 9 May 2014 / Accepted: 22 May 2014 / Published: 28 May 2014
(This article belongs to the Special Issue Information Geometry)

Abstract

We investigate the asymptotic construction of constant-risk Bayesian predictive densities under the Kullback–Leibler risk when the distributions of data and target variables are different and have a common unknown parameter. It is known that the Kullback–Leibler risk is asymptotically equal to a trace of the product of two matrices: the inverse of the Fisher information matrix for the data and the Fisher information matrix for the target variables. We assume that the trace has a unique maximum point with respect to the parameter. We construct asymptotically constant-risk Bayesian predictive densities using a prior depending on the sample size. Further, we apply the theory to the subminimax estimator problem and the prediction based on the binary regression model.
Keywords: Bayesian prediction; Fisher information; Kullback–Leibler divergence; minimax; predictive metric; subminimax estimator Bayesian prediction; Fisher information; Kullback–Leibler divergence; minimax; predictive metric; subminimax estimator
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yano, K.; Komaki, F. Asymptotically Constant-Risk Predictive Densities When the Distributions of Data and Target Variables Are Different. Entropy 2014, 16, 3026-3048.

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