Resistant selection of the smoothing parameter for smoothing splines
Statistics and Computing
Robust exponential smoothing of multivariate time series
Computational Statistics & Data Analysis
Bandwidth choice for robust nonparametric scale function estimation
Computational Statistics & Data Analysis
On robust cross-validation for nonparametric smoothing
Computational Statistics
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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 @nth 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.