One-sided cross-validation for nonsmooth regression functions

The one-sided cross-validation (OSCV) method is shown to be robust to lack of smoothness in the regression function. Two corrections for the case where the regression function has a discontinuous first derivative are proposed. Simulation results suggest that proposed modifications of the OSCV method are efficient for regression functions whose first derivative is discontinuous at more than two points. The OSCV method and its modification outperform the cross-validation method and the Ruppert-Sheather-Wand plug-in method in a data example involving a function that, potentially, has one discontinuity in its derivative.