Comparison of Two Bandwidth Selectors with Dependent Errors

Abstract

For nonparametric regression, in the case of dependent observations, cross-validation is known to be severely affected by dependence. This effect is precisely quantified through a limiting distribution for the cross-validated bandwidth. The performance of two methods, the "leave-$(2l + 1)$-out" version of cross-validation and partitioned cross-validation, which adjust for the effect of dependence on bandwidth selection is investigated. The bandwidths produced by these two methods are analyzed by further limiting distributions which reveal significantly different characteristics. Simulations demonstrate that the asymptotic effects hold for reasonable sample sizes.