Asymptotic normality of the k-NN single index regression estimator for functional weak dependence data*

被引：6
|
作者：
Mohammedi, Mustapha [1 ,2 ]
Bouzebda, Salim [3 ]
Laksaci, Ali [4 ]
Bouanani, Oussama [5 ]
机构：
[1] Univ Abdelhamid Ibn Badis Mostaganem, Mostaganem, Algeria
[2] Univ Djillali Liabes Sidi Bel Abbes, LSPS, Sidi Bel Abbes, Algeria
[3] Universie Technol Compiegne, LMAC Lab Appl Math Compiegne, CS 60 319, F-60203 Compiegne, France
[4] King Khalid Univ, Coll Sci, Dept Math, Abha, Saudi Arabia
[5] Univ Dr Moulay Tahar Saida, LMSSA, Saida, Algeria
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2024年 / 53卷 / 09期
关键词：
Asymptotic normality; k-Nearest Neighbors (k-NN; Kernel regression estimation; quasi-associated variables; single functional index model; weak dependence data; NONPARAMETRIC REGRESSION; RANDOM-VARIABLES; CONSISTENCY; ASSOCIATION; DENSITY;
D O I：
10.1080/03610926.2022.2150823
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 article, we consider the k-Nearest Neighbors (k-NN) method in a single index regression model when the explanatory variable is valued in functional space in the setting of the quasi-association dependence condition. The main result of this work is the establishment of the asymptotic distribution for the k-NN kernel single index estimator. These results are established under fairly general conditions on the underlying models. As an application, the asymptotic confidence bands for the regression model based on the single-index model are presented. Some simulation studies are carried out to show the finite sample performances of the k-NN estimator.
引用
收藏
页码：3143 / 3168
页数：26
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