Regression models with correlated errors based on functional random design

被引：7

作者：

Benhenni, Karim ^{[1
]}

Hedli-Griche, Sonia ^{[2
]}

Rachdi, Mustapha ^{[3
]}

机构：

[1] Univ Grenoble Alpes, UMR CNRS 5224, LJK, Grenoble, France

[2] Univ Setif, Setif, Algeria

[3] Univ Grenoble Alpes, AGIM Team, AGEIS EA 7407, Grenoble, France

来源：

TEST | 2017年 / 26卷 / 01期

关键词：

Random functional data; Kernel estimator; Mean squared error (MSE); Short and long memory process; Asymptotic distribution; ARFIMA and Ornstein-Uhlenbeck process; Negatively associated process; NONPARAMETRIC REGRESSION; ASYMPTOTIC NORMALITY;

D O I：

10.1007/s11749-016-0495-1

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：

This paper deals with the study of the estimation of the functional regression operator when the explanatory variable takes its values in some abstract space of functions. The main goal of this paper is to establish the exact rate of convergence of the mean squared error of the functional version of the Nadaraya-Watson kernel estimator when the errors come from a stationary process under long or short memory and based on random functional data. Moreover, these theoretical results are checked through some simulations with regular (smooth) and irregular curves and then with real data.

引用

页码：1 / 21

页数：21

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