No. 1037

Title:

Bayesian bootstrap prediction

Author(s):

Fushiki, Tadayoshi (The Institute of Statistical Mathematics)

Key words:

Bayesian bootstrap; Bootstrap; Kullback-Leibler divergence; Prediction

Abstract:

    In this paper, bootstrap prediction is adapted to resolve some problems in small sample datasets. The bootstrap predictive distribution is obtained by applying Breiman's bagging to the plug-in distribution with the maximum likelihood estimator. The effectiveness of bootstrap prediction has previously been shown, but some problems may arise when bootstrap prediction is constructed in small sample datasets. In this paper, Bayesian bootstrap is used to resolve the problems. The properties of Bayesian bootstrap prediction are studied by using the statistical asymptotic theory. The effectiveness of Bayesian bootstrap prediction is confirmed by some examples. In real data, it is shown that Bayesian bootstrap prediction provides stable prediction when the sample size is close to the dimension of the parameters.