Abstract

SUMMARY

To select a proper bandwidth is a critical step in kernel density estimation. It is well known that the bandwidth selected by cross-validation has a large variability. This difficulty limits the applicability of cross-validation. To reduce the variability, we suggested modifying the sample characteristic function beyond some cut-off frequency in estimating the bias term of the mean integrated squared error. It is proposed to select the cut-off frequency by a generalization of cross-validation. For smooth density functions, the asymptotic distribution of the bandwidth estimator based on the estimated cut-off frequency is obtained. The proposed bandwidth estimator has a relative convergence rate n−½, which is much faster than the rate n−½ for the bandwidth estimate selected by cross-validation. A modification which reduces the chance of selecting a large cut-off frequency is also suggested. In simulation studies, the advantages of the proposed procedures are clearly demonstrated. The procedures are also applied to some data sets.

You do not currently have access to this article.