非线性自回归序列L_1估计的渐近分布  

Asymptotical distribution of L_1-estimator for nonlinear autoregression

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）》2007年第4期427-432,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(60574075)

摘　　要：由于时间序列数据中经常出现的厚尾特征使得通常的估计方法不再具有渐近的正态分布,在误差项二阶矩有限的条件下考虑了非线性自回归序列的L_1估计.采用局部线性近似的方法得到了具有凸样本路径的随机过程,在此基础上利用凸样本路径随机过程弱收敛的性质证明了非线性自回归序列L_1估计的渐近正态性及无偏性.It is known that the asymptotical distribution of ordinary estimator will not be normal if the time series have the heavy tail. L1-estimators of unknown parameters in the nonlinear autoregressive model are investigated under the assumption that the error terms have the finite 2th moment.By utilizing the local linear approximation approach the stochastic processes with the convex sample path are obtained.With the properties of weak convergence of convex processes the asymptotical normality and unbiasness of L1-estimator are shown.

关 键 词：非线性自回归 L1估计 弱收敛 渐近正态 

分 类 号：O212.1[理学—概率论与数理统计]