SOME NONASYMPTOTIC BOUNDS FOR L1 DENSITY-ESTIMATION USING KERNELS

• 成果类型: Note
• 署名作者: DATTA, S
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348791
• 发表日期: 1992
• 页码: 1658-1667
• 关键词: risk

摘要

In this paper we obtain uniform upper bounds for the L1 error of kernel estimators in estimating monotone densities and densities of bounded variation. The bounds are nonasymptotic and optimal in n, the sample size. For the bounded variation class, it is also optimal wrt an upper bound of the total variation. The proofs employ a one-sided kernel technique and are extremely simple.