部分线性模型非参数分量的线性关系检验(英文)

Testing Linearity for Nonparametric Component of Partially Linear Models

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.

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 X^2 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.