Reducing the variance by smoothing

被引：11

作者：

Fernholz, LT ^{[1
]}

机构：

[1] TEMPLE UNIV,DEPT STAT,PHILADELPHIA,PA 19122

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1997年 / 57卷 / 01期

关键词：

statistical functionals; kernel estimator; influence function; smoothing; asymptotic variance;

D O I：

10.1016/S0378-3758(96)00033-X

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 show that versions of statistical functionals which are obtained by smoothing the corresponding empirical d.f. with an appropriate kernel can reduce the variance and the mean square error of the statistic. This is shown by studying the influence function of the functional. The smaller variance is achieved when the influence function is either discontinuous or piecewise linear with convexity towards the x-axis. Examples for M- and L-estimators are given.

引用

页码：29 / 38

页数：10