重尾非线性自回归模型自加权M-估计的渐近分布

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 475-483.

重尾非线性自回归模型自加权M-估计的渐近分布

傅可昂(),丁丽,李君巧

^{浙江工商大学统计与数学学院杭州 310018}

收稿日期:2018-09-27 出版日期:2020-04-26 发布日期:2020-05-21
作者简介:傅可昂, E-mail:fukeang@hotmail.com
基金资助:
国家自然科学基(11971432);浙江省自然科学基金(LY17A010004);浙江省一流学科A类(浙江工商大学统计学)

Asymptotics for the Self-Weighted M-Estimation of Nonlinear Autoregressive Models with Heavy-Tailed Errors

Keang Fu(),Li Ding,Junqiao Li

^{School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018}

Received:2018-09-27 Online:2020-04-26 Published:2020-05-21
Supported by:
the NSFC(11971432);the NSF of Zhejiang Province(LY17A010004);the First Class Discipline of Zhejiang-A(浙江工商大学统计学)

摘要/Abstract

摘要：

考虑非线性自回归模型x_t=f（x_t-1，…，x_t-p，θ）+ε_t，其中θ为q维未知参数，ε_t为随机误差.在允许误差方差无穷的重尾条件下，构造θ的自加权M-估计，并证明了该估计的渐近正态性.最后通过数值模拟，在随机误差服从某些重尾分布的条件下，说明自加权M-估计比最小二乘和L₁估计更有效.

关键词: 非线性自回归, 自加权M-估计, 重尾, 渐近正态

Abstract:

Consider the nonlinear autoregressive model x_t=f(x_t-1, …, x_t-p, θ)+ε_t, where θ is the q-dimensional unknown parameter and ε_t's are random errors with possibly infinite variance. In this paper, the self-weighted M-estimator of θ is constructed, and the asymptotic normality of the proposed estimator is also established. Some simulation studies are also given to show that the self-weighted M-estimators have good performances with some heavy-tailed random errors.

Key words: Nonlinear autoregression, Self-weighted M-estimator, Heavy tail, Asymptotic normality

中图分类号:

O212.1

傅可昂,丁丽,李君巧. 重尾非线性自回归模型自加权M-估计的渐近分布[J]. 数学物理学报, 2020, 40(2): 475-483.

Keang Fu,Li Ding,Junqiao Li. Asymptotics for the Self-Weighted M-Estimation of Nonlinear Autoregressive Models with Heavy-Tailed Errors[J]. Acta mathematica scientia,Series A, 2020, 40(2): 475-483.

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