Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis

In this paper, under a semiparametric partly linear regression model with fixed design, we introduce a family of robust procedures to select the bandwidth parameter. The robust plug-in proposal is based on nonparametric robust estimates of the ννth derivatives and under mild conditions, it converges to the optimal bandwidth. A robust cross-validation bandwidth is also considered and the performance of the different proposals is compared through a Monte Carlo study. We define an empirical influence measure for data-driven bandwidth selectors and, through it, we study the sensitivity of the data-driven bandwidth selectors. It appears that the robust selector compares favorably to its classical competitor, despite the need to select a pilot bandwidth when considering plug-in bandwidths. Moreover, the plug-in procedure seems to be less sensitive than the cross-validation in particular, when introducing several outliers. When combined with the three-step procedure proposed by Bianco and Boente [2004. Robust estimators in semiparametric partly linear regression models. J. Statist. Plann. Inference 122, 229–252] the robust selectors lead to robust data-driven estimates of both the regression function and the regression parameter.