| 部分线性模型非参数分量的线性关系检验 |
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| 引用本文： | 魏传华,吴喜之.部分线性模型非参数分量的线性关系检验[J].应用数学,2007,20(1):183-190. |
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| 作者姓名： | 魏传华 吴喜之 |
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| 作者单位： | 1. 中央民文族大学数学与计算机科学学院,北京,100081
2. 中国人民大学统计学院,北京,100872 |
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| 摘 要： | 对于部分线性模型中非参数部分是否为某一特定阶数(记为p)的多项式函数的检验问题,本文基于非参数函数在各点的p阶导函数估计值的样本方差构造了一个简单的检验统计量.给出了计算检验p-值的三阶矩χ2逼近方法.最后通过数值模拟验证了我们所提检验方法的有效性.
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| 关 键 词： | 导函数估计 部分线性模型 Profile最小二乘估计 三阶矩χ2逼近 Three-moment χ2 approximation |
| 文章编号： | 1001-9847(2007)01-0183-08 |
| 修稿时间： | 2006-06-19 |
Testing Linearity for Nonparametric Component of Partially Linear Models |
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| WEI Chuan-hua,WU Xi-zhi.Testing Linearity for Nonparametric Component of Partially Linear Models[J].Mathematica Applicata,2007,20(1):183-190. |
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| Authors: | WEI Chuan-hua WU Xi-zhi |
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| Institution: | 1. School of Mathematics and Computer- Science,Central University for Nationalities, Beijing 100081, China 2. School of Statistics, Renmin University of China, Beijing 100872, China |
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| Abstract: | In the problem of testing whether nonparametric component of a partially linear model is a polynomial of a certain degree (denote p),we propose in this article a simple test statistic which is based on sample variance of the estimated pth derivative of the nonparametric function at each design point.Three-moment χ2 approximation is employed to derive the p-value of the test.Furthermore,some simulations are conducted to examine the performance of our test procedure and the results are satisfactory. |
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| Keywords: | Derivative estimation Partially linear models Profile least-squares approach |
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