Consistency results of the M-regression function estimator for stationary continuous-time and ergodic data

被引：1

作者：

Mokhtari, Fatiha ^{[1
]}

Rouane, Rachida ^{[1
]}

Rahmani, Saadia ^{[1
]}

Rachdi, Mustapha ^{[2
]}

机构：

[1] Dr Taher Moulay Univ Saida, Lab Stochast Models Stat & Applicat, Saida 20000, Algeria

[2] Univ Grenoble Alpes, AGEIS, UFR, SHS, BP 47, Grenoble 9, France

来源：

STAT | 2022年 / 11卷 / 01期

关键词：

continuous-time processes; ergodic data; pointwise convergence; rate of convergence; robust regression; ROBUST ESTIMATOR; MODEL;

D O I：

10.1002/sta4.484

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 is devoted to the study of asymptotic properties of the kernel estimator of the robust regression function for stationary continuous-time and ergodic data. Such a dependence structure is an alternative to the strong mixing conditions usually assumed in functional time series analysis. More precisely, we consider the kernel type estimator of the robust regression function constructed from the stationary and continuous-time ergodic data (Xt,Yt) for 0 <= t <= T. Then, we establish the almost sure (with rate) pointwise convergence of this estimator. A simulation study was conducted in order to compare the performance of this method to the classical regression method.

引用

页数：18

共 50 条

[21] Nonparametric M-estimation for right censored regression model with stationary ergodic data
Chaouch, Mohamed
Laib, Naamane
Said, Elias Ould
STATISTICAL METHODOLOGY, 2016, 33 : 234 - 255
[22] Some asymptotic properties of kernel regression estimators of the mode for stationary and ergodic continuous time processes
Salim Bouzebda
Sultana Didi
Revista Matemática Complutense, 2021, 34 : 811 - 852
[23] Some asymptotic properties of kernel regression estimators of the mode for stationary and ergodic continuous time processes
Bouzebda, Salim
Didi, Sultana
REVISTA MATEMATICA COMPLUTENSE, 2021, 34 (03): : 811 - 852
[24] Large deviation results for the nonparametric regression function estimator on functional data
Louani D.
Ould Maouloud S.M.
Mathematical Methods of Statistics, 2012, 21 (4) : 298 - 313
[25] Large deviations of regression parameter estimator in continuous-time models with sub-Gaussian noise
Ivanov, Alexander V.
Orlovskyi, Igor V.
MODERN STOCHASTICS-THEORY AND APPLICATIONS, 2018, 5 (02): : 191 - 206
[26] Multivariate wavelet density and regression estimators for stationary and ergodic discrete time processes: Asymptotic results
Bouzebda, Salim
Didi, Sultana
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (03) : 1367 - 1406
[27] Welch-Type Estimator for a Spectral Density Function. Case of a Continuous-Time
Alekseev, V. G.
Sukhodoev, V. A.
OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING, 2009, 45 (02) : 107 - 112
[28] Welch-type estimator for a spectral density function. Case of a continuous-time
V. G. Alekseev
V. A. Sukhodoev
Optoelectronics, Instrumentation and Data Processing, 2009, 45 (2) : 107 - 112
[29] Empirical Hazard Function Using Continuous-Time Failure Data
Xie, Gang
Li, Fengfeng
Sun, Yong
Ma, Lin
PROCEEDINGS OF THE 7TH WORLD CONGRESS ON ENGINEERING ASSET MANAGEMENT (WCEAM 2012), 2015, : 647 - 656
[30] On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models
A. V. Ivanov
N. N. Leonenko
I. V. Orlovskyi
Statistical Inference for Stochastic Processes, 2020, 23 : 129 - 169

← 1 2 3 4 5 →