AN AUTOMATIC BANDWIDTH SELECTOR FOR KERNEL DENSITY-ESTIMATION

• 成果类型: Article
• 署名作者: CHIU, ST
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/79.4.771
• 发表日期: 1992
• 页码: 771782
• 关键词: squares cross-validation; empirical choice; histograms; error

摘要

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-1/2, 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.