| 重尾非线性自回归模型自加权M-估计的渐近分布 |
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| 引用本文： | 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(A辑),2020(2):475-483. |
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| 作者姓名： | 傅可昂 丁丽 李君巧 |
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| 作者单位： | 浙江工商大学统计与数学学院 |
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| 基金项目： | 国家自然科学基金(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)。 |
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| 摘 要： | 考虑非线性自回归模型xt=f(xt-1,…,xt-p,θ)+∈t,其中θ为q维未知参数,{∈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.
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| 关 键 词： | 非线性自回归 自加权M-估计 重尾 渐近正态 |
Asymptotics for the Self-Weighted M-Estimation of Nonlinear Autoregressive Models with Heavy-Tailed Errors |
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| Fu Keang,Ding Li,Li Junqiao.Asymptotics for the Self-Weighted M-Estimation of Nonlinear Autoregressive Models with Heavy-Tailed Errors[J].Acta Mathematica Scientia,2020(2):475-483. |
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| Authors: | Fu Keang Ding Li Li Junqiao |
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| Institution: | (School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018) |
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| Abstract: | Consider the nonlinear autoregressive model xt=f(xt-1,…,xt-p,θ)+∈t,whereθis the q-dimensional unknown parameter and∈t’s are random errors with possibly infinite variance.In this paper,the self-weighted M-estimator ofθis 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. |
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| Keywords: | Nonlinear autoregression Self-weighted M-estimator Heavy tail Asymptotic normality |
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