FDA: strong consistency of the kNN local linear estimation of the functional conditional density and mode

被引：23

作者：

Chikr-Elmezouar, Zouaoui ^{[1
]}

Almanjahie, Ibrahim M. ^{[1
]}

Laksaci, Ali ^{[1
]}

Rachdi, Mustapha ^{[2
]}

机构：

[1] King Khalid Univ, Coll Sci, Dept Math, Abha, Saudi Arabia

[2] Univ Grenoble Alpes, Lab AGEIS EA 7407, TIMB Team, UFR SHS, BP 47, F-38040 Grenoble 09, France

来源：

JOURNAL OF NONPARAMETRIC STATISTICS | 2019年 / 31卷 / 01期

关键词：

Functional data analysis; nonparametric functional data analysis; almost-complete convergence; local linear estimation; conditional mode; Kernel method; conditional density function; k-nearest neighbours method; NONPARAMETRIC REGRESSION; ASYMPTOTIC NORMALITY; ERROR; SINGLE;

D O I：

10.1080/10485252.2018.1538450

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 present a new estimator of the conditional density and mode when the co-variables are of functional kind. This estimator is a combination of both, the k-Nearest Neighbours procedure and the functional local linear estimation. Then, for each statistical parameter (conditional density or mode), results concerning the strong consistency and rate of convergence of the estimators are presented. Finally, their performances, for finite sample sizes, are illustrated by using simulated data.

引用

页码：175 / 195

页数：21

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