Chiu, Shean-Tsong An automatic bandwidth selector for kernel density estimation. (English) Zbl 0764.62034 Biometrika 79, No. 4, 771-782 (1992). 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 \(n^{-{1\over 2}}\), which is much faster than the rate \(n^{-1/10}\) 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. Cited in 14 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics Keywords:kernel density estimation; sample characteristic function; bias term; mean integrated squared error; cut-off frequency; generalization of cross-validation; bandwidth estimator; relative convergence rate; simulation studies PDFBibTeX XMLCite \textit{S.-T. Chiu}, Biometrika 79, No. 4, 771--782 (1992; Zbl 0764.62034) Full Text: DOI