方差无穷非线性自回归序列的自加权L_1估计  

Self-weighted L_1-estimator for infinite variance nonlinear autoregressive model

作　　者：周杰[1] 刘三阳[1] 张正策[2] 

机构地区：[1]西安电子科技大学应用数学系,陕西西安710071 [2]西安交通大学数学系,陕西西安710065

出　　处：《高校应用数学学报（A辑）》2008年第2期193-199,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(60574075)

摘　　要：对具有无穷方差的非线性自回归序列x_t=φ(x_(t-1),x_(t-2),…,x_(t-p),θ)+ε_t,E(ε_t^2)=∞,利用局部二次近似和连续函数空间C(R^q)上弱收敛随机过程最小点的渐近性质,证明了若存在δ≥1,使得E|ε_t|~δ<∞成立,则θ满足一定条件的自加权L_1估计θ_(L_1)是渐近正态估计,Wald检验统计量也具有通常的x^2分布,为模型的统计推断提供了理论基础.For the nonlinear autoregressive time series model x_t=φ(x_(t-1),x_(t-2),…,x_(t-p))+ε_t with E(ε_t^2)=∞,it is showed that if there existsδ≥1 such that E|ε|~δ<∞,then the distribution ofθ_(L_1),the self-weighted L_1-estimator ofθ,is asymptotically normal and the Wald test statistic has the ordinary X^2 distribution.The local quadratic approximation and the asymptotics for the minimisers of stochastic process defined on C(R^q) are involved in the proof of theorems.

关 键 词：非线性自回归 自加权L_1估计 弱收敛 渐近正态 Wald检验统计量 

分 类 号：O212.1[理学—概率论与数理统计]