On practical implementation of the fully robust one-sided cross-validation method in the nonparametric regression and density estimation contexts

The fully robust one-sided cross-validation (OSCV) method has versions in the nonparametric regression and density estimation settings. It selects the consistent bandwidths for estimating the continuous regression and density functions that might have finitely many discontinuities in their first derivatives. The theoretical results underlying the method were thoroughly elaborated in the preceding publications, while its practical implementations needed improvement. In particular, until this publication, no appropriate implementation of the method existed in the density estimation context. In the regression setting, the previously proposed implementation has a serious disadvantage of occasionally producing the irregular OSCV functions that complicates the bandwidth selection procedure. In this article, we make a substantial progress towards resolving the aforementioned issues by proposing a suitable implementation of fully robust OSCV for density estimation and providing specific recommendations for the further improvement of the method in the regression setting.