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

作者：Yano Keisuke^*; Komaki Fumiyasu

来源：Entropy, 2014, 16(6): 3026-3048.

DOI：10.3390/e16063026

• Bayesian prediction
• Fisher information
• Kullback-Leibler divergence
• minimax
• predictive metric
• subminimax estimator

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.

• 出版日期2014-6