On estimating distribution functions using Bernstein polynomials

被引：73

作者：

Leblanc, Alexandre ^{[1
]}

机构：

[1] Univ Manitoba, Dept Stat, Winnipeg, MB R3T 2N2, Canada

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2012年 / 64卷 / 05期

关键词：

Bernstein polynomials; Distribution function estimation; Mean integrated squared error; Mean squared error; Asymptotic properties; Efficiency; Deficiency; DENSITY-ESTIMATION; BANDWIDTH SELECTION; SMOOTH ESTIMATION; CONSISTENCY;

D O I：

10.1007/s10463-011-0339-4

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：

It is a known fact that some estimators of smooth distribution functions can outperform the empirical distribution function in terms of asymptotic (integrated) mean-squared error. In this paper, we show that this is also true of Bernstein polynomial estimators of distribution functions associated with densities that are supported on a closed interval. Specifically, we introduce a higher order expansion for the asymptotic (integrated) mean-squared error of Bernstein estimators of distribution functions and examine the relative deficiency of the empirical distribution function with respect to these estimators. Finally, we also establish the (pointwise) asymptotic normality of these estimators and show that they have highly advantageous boundary properties, including the absence of boundary bias.

引用

页码：919 / 943

页数：25