A universally acceptable smoothing factor for kernel density estimates

• 成果类型: Article
• 署名作者: Devroye, L; Lugosi, G
• 署名单位: Budapest University of Technology & Economics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 2499-2512
• 关键词: convergence; distance; rates; RISK; histograms; L1

摘要

We define a minimum distance estimate of the smoothing factor for kernel density estimates, based on a methodology first developed by Yatracos. It is shown that if f(nh) denotes the kernel density estimate on R(d) for an i.i.d. sample of size n drawn from an unknown density f, where h is the smoothing factor, and if f(n) is the kernel estimate with the same kernel and with the proposed new data-based smoothing factor, then, under a regularity condition on the kernel K, sup lim sup/fn-->infinity E integral\f(n)-f\dx/inf(h>0)E integral\f(nh)-f\dx This is the first published smoothing factor that can be proven to have this property.