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Journal of Shanghai University >

2018 , Vol. 24 >Issue 6: 1022 - 1029

DOI: https://doi.org/10.12066/j.issn.1007-2861.1926

Research Paper

Bayesian estimation for nonparametric regression

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  • College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2017-02-15

  Online published: 2018-12-26

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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

Cite this article

SU Yaling, HE Youhua . Bayesian estimation for nonparametric regression[J]. Journal of Shanghai University, 2018 , 24(6) : 1022 -1029 . DOI: 10.12066/j.issn.1007-2861.1926

References

[1] Devroye L. The uniform convergence of the Nadaraya-Watson regression function estimate[J]. Canadian Journal of Statistics, 1978,6(2):179-191.
[2] Greblicki W, Pawlak M. Distribution-free pointwise consistency of kernel regressionestimate[J]. J Annals of Statistics, 1984,12(4):1570-1575.
[3] Devroye L. On the almost everywhere convergence of nonparametric regression function estimates[J]. J Annals of Statistics, 1981,9(6):1310-1319.
[4] Fan J Q. Local linear regression smoothers and their minimax efficiencies[J]. J Annals of Statistics, 1993,21(1):196-216.
[5] Antoniadis A, Gregoire G, McKeague I W. Wavelet methods for curve estimation[J]. Journal of the American Statistical Association, 1994,89(428):1340-1353.
[6] Ferguson T. A Bayesian analysis of some nonparametric problems[J]. J Annals of Statistics, 1973,1(2):209-230.
[7] Jayaram S. A constructive definition of Dirichlet priors[J]. J Statistics Sinica, 1994,4(2):639-650.
[8] 姚宗静. 基于 Dirichlet 过程的非参数贝叶斯分析[D]. 成都: 西南交通大学, 2007.
[9] 龙杏芬, 张德生, 武新乾. 非参数回归模型的贝叶斯局部线性估计[J]. 山西大学学报(自然科学版), 2010,33(3):371-374.
[10] 卢一强, 茆诗松. 广义非参数回归的 B 样本贝叶斯估计[J]. 应用数学, 2015,18(1):8-13.
[11] 沃塞曼. 现代数学译丛 3: 现代非参数统计 [M]. 北京: 科学出版社, 2008: 58-65.
[12] Hardle W, Werwatz A, Müller M, et al. Nonparametric and semiparametric models[J]. Springer Series in Statistics, 2006,62(2):628-629.
[13] Ruppert D, Wand M P. Multivariate locally weighted least squares regression[J]. Annals of Statistics, 1994,22(3):1346-1370.
[14] 王学保, 蔡果兰. Logistic 模型的参数估计及人口预测[J]. 北京工商大学学报(自然科学版), 2009,27(6):75-78.
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