One-sided cross-validation (OSCV) is a bandwidth selection method initially introduced by Hart and Yi (J Am Stat Assoc 93(442):620–631, 1998) in the context of smooth regression functions. Martínez-Miranda et al. (in Gregoriou (ed) Operational risk towards basel III: best practices and issues in modeling, management and regulation, Wiley, Hoboken, 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 performance in the regression context.

中文翻译：

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非平滑密度函数的单面交叉验证

单边交叉验证（OSCV）是一种带宽选择方法，最初是由Hart和Yi引入的（在平滑回归函数的背景下，J Am Stat Assoc 93（442）：620-631，1998）。Martínez-Miranda等。（Gregoriou（ed），《巴塞尔协议三》的操作风险：建模，管理和监管方面的最佳实践和问题，Wiley，Hoboken，2009年）开发了一种OSCV版本，用于平滑密度函数。本文扩展了非光滑密度的方法。它还引入了完全健壮的OSCV修改，可在平滑和非平滑情况下产生一致的OSCV带宽。讨论了用于平滑和非平滑密度的OSCV方法的实际实现。被认为是交叉验证内核之一，有潜力在回归环境中提高OSCV方法的性能。