| 非参数Bayes样条回归 |
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| 引用本文： | 卢一强,茆诗松.非参数Bayes样条回归[J].华东师范大学学报(自然科学版),2004,2004(4):33-39,90. |
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| 作者姓名： | 卢一强 茆诗松 |
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| 作者单位： | 信息工程大学,电子技术学院,郑州,450004;华东师范大学,统计系,上海,200062;华东师范大学,统计系,上海,200062 |
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| 基金项目： | 国家自然科学基金(10271078) |
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| 摘 要： | 对于非参数回归模型y= f(x)+ε，其中f (x)为光滑的连续函数.用样条函数来逼近f (x)，不具体选择结点的个数，考虑到结点个数的不确定性，给定结点个数一个均匀的无信息先验，用Bayes模型平均的方法来估计f (x).得到了f (x)的Bayes估计和Bayes后验区间估计.
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| 关 键 词： | Bayes模型平均 可逆的跳MCMC抽样 样条回归 Bayes因子 |
| 文章编号： | 1000-5641(2004)04-0033-07 |
| 收稿时间： | 2002-9-30 |
| 修稿时间： | 2003-4-25 |
Bayesian Spline Nonparametric Regression |
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| LU Yi-qiang,MAO Shi-song.Bayesian Spline Nonparametric Regression[J].Journal of East China Normal University(Natural Science),2004,2004(4):33-39,90. |
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| Authors: | LU Yi-qiang MAO Shi-song |
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| Institution: | 1. Institute of Electronic Technology，Information Engineering University，Zhengzhou 450004,China ; 2. Department of Statistics，East China Normal University，Shanghai 200062，China |
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| Abstract: | In this paper the nonparametric regression model y= f(x)+ε, where f (x) is a smoothing function, is considered. The nonparametric regression f (x) is approximated by a spline function. The knot number is not fixed but given a noninformation prior, by which the uncertainty of the knot number is studied. The regression f(x) is estimated by the method of Bayesian model averaging and the posterior interval is also estimated. |
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| Keywords: | Bayesian model averaging reversible jumped MCMC sampling spline regression Bayes factor |
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