No. 919

Title:

Bootstrap prediction and Bayesian prediction under misspecified models

Author(s):

Fushiki, Tadayoshi (The Institute of Statistical Mathematics)

Key words:

Bagging; Bayesian prediction; Kullback-Leibler divergence; Misspecified models

Abstract:

    In this paper, we consider a statistical prediction problem under misspecified models. In a sense, Bayesian prediction is an optimal prediction method when an assumed model is true. Bootstrap prediction is obtained by applying Breiman's bagging method to a plug-in prediction and can be considered to be an approximation of the Bayesian prediction under the assumption that the model is true. Under misspecified models, we show that bootstrap prediction is asymptotically more effective than Bayesian prediction. This means that bootstrap prediction is a robust prediction method.