Theoretical Properties and Practical Performance of Fully Robust One-Sided Cross-Validation

Fully robust OSCV is a modification of the OSCV method that produces consistent bandwidth in the cases of smooth and nonsmooth regression functions. The current implementation of the method uses the kernel $H_I$ that is almost indistinguishable from the Gaussian kernel on the interval $[-4,4]$, but has negative tails. The theoretical properties and practical performances of the $H_I$- and $ϕ$-based OSCV versions are compared. The kernel $H_I$ tends to produce too low bandwidths in the smooth case. The $H_I$-based OSCV curves are shown to have wiggles appearing in the neighborhood of zero. The kernel $H_I$ uncovers sensitivity of the OSCV method to a tiny modification of the kernel used for the cross-validation purposes. The recently found robust bimodal kernels tend to produce OSCV curves with multiple local minima. The problem of finding a robust unimodal nonnegative kernel remains open.

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