No. 1075

Title:

Bayesian Prediction of a Density Function in Terms of $e$-Mixture

Author(s):

Yanagimoto, Takemi (Chuo University);
Ohnishi, Toshio (The Institute of Statistical Mathematics)

Key words:

Conjugate prior; Dual structure; Jeffreys' prior; Pythagorean relationship; Plug-in predictor

Abstract:

    The optimum Bayesian predictor under the $e$-divergence loss is proposed and discussed. Notable dualistic structure is observed between the proposed predictor and the optimum predictor under the $m$-divergence loss, the latter of which is dominantly discussed in the existing literature. An advantage of the proposed optimum predictor is that it is estimative, when the sampling density is in the exponential family. Potential advantages of the proposed predictor over its dual one are discussed, which include the shrinkage estimator, the model selection problem and the likelihood ratio. Further, we emphasize potential usefulness of the use of Jeffreys' prior.