重尾非线性自回归模型自加权M-估计的渐近分布  

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

作　　者：傅可昂[1] 丁丽 李君巧 Fu Keang;Ding Li;Li Junqiao(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018

出　　处：《数学物理学报（A辑）》2020年第2期475-483,共9页Acta Mathematica Scientia

基　　金：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)。

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.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.

关 键 词：非线性自回归 自加权M-估计 重尾 渐近正态 

分 类 号：O212.1[理学—概率论与数理统计]