On local asymptotic normality for functional autoregressive processes

被引：5

作者：

Kara-Terki, Nesrine ^{[1
]}

Mourid, Tahar ^{[1
]}

机构：

[1] Univ Abou Bekr Belkaid Tlemcen, Lab Stat & Modelisat Aleatoires, Tilimsen 13000, Algeria

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2016年 / 148卷

关键词：

Functional autoregressive processes; Local asymptotic normality; Hajek bound; Maximum likelihood estimator; Efficiency; LIKELIHOOD FUNCTION; TIME-SERIES;

D O I：

10.1016/j.jmva.2016.02.017

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：

We establish Local Asymptotic Normality (LAN) and Uniform Local Asymptotic Normality (ULAN) conditions for a class of function space valued autoregressive processes when the correlation operator depends on an unknown one-dimensional parameter. We then derive Hajek minimax bound, consistency, asymptotic normality and efficiency of the conditional maximum likelihood estimator yielding their optimality. A simulation studies illustrate the performance of the estimators. (c) 2016 Elsevier Inc. All rights reserved.

引用

页码：120 / 140

页数：21

共 50 条

[1] Tests in functional autoregressive processes via local asymptotic normality condition
Nesrine, Kara-Terki
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2023, 53 (23) : 8556 - 8570
[2] Local asymptotic normality of Hilbertian autoregressive processes
Kara-Terki, Nesrine
Mourid, Tahar
[J]. COMPTES RENDUS MATHEMATIQUE, 2016, 354 (06) : 634 - 638
[3] Asymptotic Normality of Autoregressive Processes
Miao, Yu
[J]. ACTA APPLICANDAE MATHEMATICAE, 2010, 110 (03) : 1077 - 1085
[4] Asymptotic Normality of Autoregressive Processes
Yu Miao
[J]. Acta Applicandae Mathematicae, 2010, 110 : 1077 - 1085
[5] The local asymptotic normality of a class of generalized random coefficient autoregressive processes
Hwang, SY
Basawa, IV
[J]. STATISTICS & PROBABILITY LETTERS, 1997, 34 (02) : 165 - 170
[6] Local asymptotic normality of truncated empirical processes
Falk, M
[J]. ANNALS OF STATISTICS, 1998, 26 (02): : 692 - 718
[7] On Asymptotic Normality of Sequential LS-Estimates of Unstable Autoregressive Processes
Galtchouk, L.
Konev, V.
[J]. SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS, 2011, 30 (02): : 117 - 144
[8] Local asymptotic normality for the scale parameter of stable processes
Woerner, JHC
[J]. STATISTICS & PROBABILITY LETTERS, 2003, 63 (01) : 61 - 65
[9] Conditions of Local Asymptotic Normality for Gaussian Stationary Processes
V. N. Solev
A. Zerbet
[J]. Journal of Mathematical Sciences, 2003, 118 (6) : 5635 - 5649
[10] LOCAL ASYMPTOTIC NORMALITY FOR MULTIVARIATE LINEAR-PROCESSES
WANG, XB
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1994, 49 (02) : 331 - 345

← 1 2 3 4 5 →