Nonparametric Testing in Regression Models with Wilcoxon-type Generalized Likelihood Ratio

The generalized likelihood ratio (GLR) statistic (Fan, Zhang, and Zhang (2001)) offered a generally applicable method for testing nonparametric hypotheses about nonparametric functions, but its efficiency is adversely affected by outlying observations and heavy-tailed distributions. Here a robust testing procedure is developed under the framework of the GLR by incorporating a Wilcoxon-type artificial likelihood function, and adopting the associated local smoothers. Under some useful hypotheses, the proposed test statistic is 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 t-test. Simulation results are consistent with the asymptotic analysis.