相依样本下污染线性模型的最近邻估计  

The Nearest Neighbor Estimation In Contaminated Linear Model Under Dependent Samples

作　　者：柴根象[1] 吴月琴[1] 

机构地区：[1]同济大学应用数学系,上海200092

出　　处：《应用数学学报》2006年第3期542-554,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10171079号)资助项目~~

摘　　要：考虑一般线性模型,设误差序列{ei}是平稳的α-混合序列,具有公共未知密度,f(x)．本文首先讨论了基于残差的f(x)的最近邻估计的相合性及收敛速度,然后把结论推广到污染线性模型,讨论了污染系数ε,误差的主体分布及回归系数β的估计的相合性,收敛速度以及(β|^)的渐近正态性．For a linear model, let the error sequence {ei} is stationary α-mixing sequence and has an unknown density f（x）. In this paper, we study the consistency and convergence rate of the nearest neighbor estimation of f（x） based on the residuals. Then the result is extended to the contaminated linear model. The estimation of contaminated coefficient ε, the main distribution of error f（x） and the regression parameter β are established, and the consistency and convergence rate of these estimators are obtained too. Moreover, the asymptotic normality of β^ is gained.

关 键 词：污染线性模型 Α-混合 最近邻估计 相合性 收敛速度 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]