Robust comparison of regression curves

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 the (Formula presented.)(Formula presented.) test. We then consider a bootstrap approximation to determine (Formula presented.)(Formula presented.) values 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.