非参数回归的贝叶斯估计

doi:10.12066/j.issn.1007-2861.1926

上海大学学报(自然科学版) ›› 2018, Vol. 24 ›› Issue (6): 1022-1029.doi: 10.12066/j.issn.1007-2861.1926

非参数回归的贝叶斯估计

苏雅玲, 何幼桦()

上海大学理学院, 上海 200444

收稿日期:2017-02-15 出版日期:2018-12-30 发布日期:2018-12-26
通讯作者: 何幼桦 E-mail:heyouhua@shu.edu.cn
基金资助:
国家自然科学基金资助项目(11371242)

Bayesian estimation for nonparametric regression

SU Yaling, HE Youhua()

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2017-02-15 Online:2018-12-30 Published:2018-12-26
Contact: HE Youhua E-mail:heyouhua@shu.edu.cn

摘要/Abstract

摘要：

基于因变量 $Y$ 对自变量 ${X}$ 条件分布的非参数贝叶斯估计, 通过期望计算得到未知回归函数的后验估计表达式, 并计算出估计的均方误差, 证明该估计的均方收敛性. 阐明当先验的选择接近真实的回归函数时, 该估计的均方误差小于局部线性核回归的均方误差. 最后通过实证分析, 表明该非参数贝叶斯回归比非参数局部线性回归具有更好的预测效果.

关键词: 非参数贝叶斯回归, 非参数贝叶斯分布估计, Dirichlet过程, 局部线性回归, 人口预测

Abstract:

Based on nonparametric Bayesian estimation of a conditional distribution, posterior estimation of an unknown regression function is obtained by calculating its expectation. The mean square error of the estimation is calculated. Its convergence in mean square of the estimation is proved. It is shown that the mean square error of the estimation is less than that of the local linear kernel regression when prior regression is chosen to be close to the unknown regression function. Empirical evidence shows that the nonparametric Bayesian regression may be more effective in prediction than local linear regression.

Key words: nonparametric Bayesian regression, nonparametric Bayesian distribution estimation, Dirichlet process, local linear regression, population prediction

中图分类号:

O212.7

苏雅玲, 何幼桦. 非参数回归的贝叶斯估计[J]. 上海大学学报(自然科学版), 2018, 24(6): 1022-1029.

SU Yaling, HE Youhua. Bayesian estimation for nonparametric regression[J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(6): 1022-1029.

图/表 4

参考文献 14

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非参数回归的贝叶斯估计

Bayesian estimation for nonparametric regression

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