# One-Sided Cross-Validation for Nonsmooth Density Functions

## TL;DR

This paper extends the one-sided cross-validation (OSCV) method to nonsmooth density functions and introduces a robust version that works consistently for both smooth and nonsmooth cases, with practical implementation insights.

## Contribution

It develops a new OSCV extension for nonsmooth densities and proposes a fully robust modification applicable to all density types.

## Key findings

- The robust OSCV method provides consistent bandwidths for smooth and nonsmooth densities.
- Implementation strategies improve the practical application of OSCV.
- Potential kernel improvements can enhance regression context performance.

## Abstract

One-sided cross-validation (OSCV) is a bandwidth selection method initially introduced by Hart and Yi (1998) in the context of smooth regression functions. Mart\'{\i}nez-Miranda et al. (2009) developed a version of OSCV for smooth density functions. This article extends the method for nonsmooth densities. It also introduces the fully robust OSCV modification that produces consistent OSCV bandwidths for both smooth and nonsmooth cases. Practical implementations of the OSCV method for smooth and nonsmooth densities are discussed. One of the considered cross-validation kernels has potential for improving the OSCV method's implementation in the regression context.