SOME NONASYMPTOTIC BOUNDS FOR L1 DENSITY-ESTIMATION USING KERNELS

被引：7
|
作者：
DATTA, S
机构：
来源：
ANNALS OF STATISTICS | 1992年 / 20卷 / 03期
关键词：
MONOTONE DENSITY; DENSITY OF BOUNDED VARIATION; L1; ESTIMATION; MINIMAX RISK; KERNEL ESTIMATOR; NONASYMPTOTIC BOUND;
D O I：
10.1214/aos/1176348791
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：1658 / 1667
页数：10
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