部分线性模型非参数部分的多项式关系检验

Testing Polynomial Relationships of the Nonparametric Component in 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的多项式函数的检验问题,本文基于比较原假设与备择假设下模型拟合的残差平方和的思想构造了检验统计量,给出了计算检验p-值的精确方法和三阶矩χ2逼近方法。另外我们讨论了广义似然比检验统计量的构造,并给出了其在原假设下的渐近分布。最后通过数值模拟验证了我们所提检验方法的有效性。

To test whether the nonparametric component of a partially linear model is a polynomial of a certain degree, we propose in this article a test statistic which is based on the comparision of the residual sum of squares under null and alternative hypotheses. A procedure for computing the exact pvalue of the test is proposed. For computational consideration in practice, a method to approximate the p-value is derived by employing the three-moment χ^2 approximation. We also construct a generalized likelihood ratio statistic, and its asymptotic null distribution is established. Finally, some simulations are conducted to examine the performance of our test procedure and the results are satisfactory.