Robust comparison of regression curves
Robust comparison of regression curves
复制标题
回归曲线的稳健比较
DOI：
10.1007/s11749-014-0394-2
复制
发表时间：
2015
期刊：
影响因子：
1.3
通讯作者：
Zhu Lixing
中科院分区：
文献类型：
--
作者：
Feng Long;Zou Changliang;Wang Zhaojun;Zhu Lixing
本文研究两条回归曲线的稳健性比较。文献中的大多数方法都是基于最小二乘的方法，局部多项式逼近于非参数回归。然而，这些方法的效率受到异常观测和重尾分布的不利影响。为了应对这一挑战，在广义似然比检验(GLR)的框架下，通过结合Wilcoxon类型的人工似然函数，推荐了一种稳健的检验过程。在零假设下，证明了所提出的检验统计量是渐近正态的，并且没有公害参数和协变量设计。它相对于基于最小二乘的GLR方法的渐近相对效率与符号秩Wilcoxon检验的渐近相对效率密切相关。然后，我们考虑在有限样本情况下用Bootstrap近似来确定检验的值。并给出了它的渐近有效性。进行了模拟研究，以检验所提出的测试的性能，并将其与文献中的竞争对手进行比较。
This paper is concerned about robust comparison of two regression curves. Most of the procedures in the literature are least-squares-based methods with local polynomial approximation to nonparametric regression. However, the efficiency of these methods is adversely affected by outlying observations and heavy-tailed distributions. To attack this challenge, a robust testing procedure is recommended under the framework of the generalized likelihood ratio test (GLR) by incorporating with a Wilcoxon-type artificial likelihood function. Under the null hypothesis, the proposed test statistic is proved to be asymptotically normal and free of nuisance parameters and covariate designs. Its asymptotic relative efficiency with respect to the least-squares-based GLR method is closely related to that of the signed-rank Wilcoxon test in comparison with thetest. We then consider a bootstrap approximation to determinevalues of the test in finite sample situation. Its asymptotic validity is also presented. A simulation study is conducted to examine the performance of the proposed test and to compare it with its competitors in the literature.