Bernoulli

  • Bernoulli
  • Volume 11, Number 4 (2005), 747-758.

Bootstrap prediction and Bayesian prediction under misspecified models

Tadayoshi Fushiki

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Abstract

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. Bootstrap prediction can be considered to be an approximation to the Bayesian prediction under the assumption that the model is true. However, in applications, there are frequently deviations from the assumed model. In this paper, both prediction methods are compared by using the Kullback-Leibler loss under the assumption that the model does not contain the true distribution. We show that bootstrap prediction is asymptotically more effective than Bayesian prediction under misspecified models.

Article information

Source
Bernoulli, Volume 11, Number 4 (2005), 747-758.

Dates
First available in Project Euclid: 7 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1126126768

Digital Object Identifier
doi:10.3150/bj/1126126768

Mathematical Reviews number (MathSciNet)
MR2158259

Zentralblatt MATH identifier
1092.62042

Keywords
bagging Bayesian prediction bootstrap Kullback-Leibler divergence misspecification prediction

Citation

Fushiki, Tadayoshi. Bootstrap prediction and Bayesian prediction under misspecified models. Bernoulli 11 (2005), no. 4, 747--758. doi:10.3150/bj/1126126768. https://projecteuclid.org/euclid.bj/1126126768


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