Comparison of Two Bandwidth Selectors with Dependent Errors

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-(2e+1)-out" version of cross-validation and partitioned cross-validation. which adjust for the dependence effect 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. AMS 1980 subject classifications: Primary 62G05; secondary 62G20. Keywards: cross-validation. autoregressive-moving average process. bandwidth selector. nonparametric regression. IThis research is part of the Ph. D. dissertation of the first author, under the supervision of the second at the University of North Carolina, Chapel Hill. It was partially supported by NSF Grant DMS-8701201.