Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient

被引：0
|
作者：
Wang, Xinghui [1 ,2 ]
Geng, Wenjing [1 ]
Han, Ruidong [3 ]
Xu, Qifa [2 ]
机构：
[1] Anhui Univ, Sch Big Data & Stat, Hefei 230601, Peoples R China
[2] Hefei Univ Technol, Sch Management, Hefei 230009, Peoples R China
[3] Renmin Univ China, Sch Stat, Beijing 100872, Peoples R China
来源：
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2023年 / 25卷 / 01期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Limit distribution; Moderate deviations; M-estimate; Unit root; MODERATE DEVIATIONS; LIMIT THEORY; MODELS;
D O I：
10.1007/s11009-023-10005-6
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 consider a first-order autoregressive process with a general autoregressive coefficient. Asymptotic behaviors of an M-estimator of the autoregressive coefficient are established for the nearly stationary and mildly explosive cases, respectively. The rate of convergence of the robust estimators for the two cases are provided. The results extend ones for the least squares and least absolute deviation estimators to the robust estimator under the weaker initial conditions in the literature. Some simulations are carried out to assess the performance of our procedure.
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页数：23
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