## 抄録

We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function. Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the unknown mean is fixed, the covariance of future samples can be different from that of training samples. We show that the Bayesian predictive distribution based on the uniform prior is dominated by that based on a class of priors if the prior distributions for the covariance and future covariance matrices are rotation invariant. Then, we consider a class of priors for the mean parameters depending on the future covariance matrix. With such a prior, we can construct a Bayesian predictive distribution dominating that based on the uniform prior. Lastly, applying this result to the prediction of response variables in the Normal linear regression model, we show that there exists a Bayesian predictive distribution dominating that based on the uniform prior. Minimaxity of these Bayesian predictions follows from these results.

本文言語 | English |
---|---|

ページ（範囲） | 1888-1905 |

ページ数 | 18 |

ジャーナル | Journal of Multivariate Analysis |

巻 | 99 |

号 | 9 |

DOI | |

出版ステータス | Published - 2008 10月 |

外部発表 | はい |

## ASJC Scopus subject areas

- 統計学および確率
- 数値解析
- 統計学、確率および不確実性