Smooth conditional distribution estimators using Bernstein polynomials

被引：9

作者：

Belalia, Mohamed ^{[1
]}

Bouezmarni, Taoufik ^{[1
]}

Leblanc, Alexandre ^{[2
]}

机构：

[1] Univ Sherbrooke, Dept Math, Sherbrooke, PQ, Canada

[2] Univ Manitoba, Dept Stat, Winnipeg, MB, Canada

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 2017年 / 111卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Bernstein polynomials; Conditional distribution estimation; Mean squared error; Asymptotic properties; DENSITY-ESTIMATION; NONPARAMETRIC-ESTIMATION; QUANTILE FUNCTIONS; REGRESSION; CURVES;

D O I：

10.1016/j.csda.2017.02.005

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In a variety of statistical problems, estimation of the conditional distribution function remains a challenge. To this end, a two-stage Bernstein estimator for conditional distribution functions is introduced. The method consists in smoothing a first-stage Nadaraya-Watson or local linear estimator by constructing its Bernstein polynomial. Some asymptotic properties of the proposed estimator are derived, such as its asymptotic bias, variance and mean squared error. The asymptotic normality of the estimator is also established under appropriate conditions of regularity. Lastly, the performance of the proposed estimator is briefly studied through a few examples. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：166 / 182

页数：17

共 27 条

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[2]

[Anonymous], 2002, APPROXIMATION THEORE

[3]

[Anonymous], 1964, Sankhya, DOI DOI 10.2307/25049340

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