Data-Driven Bandwidth Choice for Density Estimation Based on Dependent Data

Abstract

The bandwidth selection problem in kernel density estimation is investigatedin situations where the observed data are dependent. The classicalleave-out technique is extended, and thereby a class of cross-validatedbandwidths is defined. These bandwidths are shown to be asymptoticallyoptimal under a strong mixing condition. The leave-one out, or ordinary,form of cross-validation remains asymptotically optimal under thedependence model considered. However, a simulation study shows thatwhen the data are strongly enough correlated, the ordinary versionof cross-validation can be improved upon in finite-sized samples.