部分线性单指标模型的M-估计  

M-ESTIMATORS IN A PARTIAL LINEAR SINGLE-INDEX MODEL

作　　者：邹清明[1] 朱仲义[2] ZOU Qingming ZHU Zhongyi(School of Economics and Management, University of South China, Hengyang 421001 Department of Statistics, Fudan University, Shanghai 200433)

机构地区：[1]湖南南华大学经济管理学院,衡阳421001 [2]复旦大学统计系,上海200433

出　　处：《系统科学与数学》2016年第11期2099-2117,共19页Journal of Systems Science and Mathematical Sciences

基　　金：教育部人文社科基金(11YJA91009)资助课题

摘　　要：单指标模型是一类非常重要的半参数回归模型,不仅可以降低数据维数,克服多元数据中的"维数祸根"问题,而且能抓住高维数据的主要特征.文章研究部分线性单指标模型的M-估计,利用B-样条近似技术逼近非参数函数,提出了获得模型中未知参数M-估计的方法,在一些正则条件下,研究了回归函数以及回归系数的M-估计的渐近性质.随机模拟结果表明了文中M-估计具有稳健性.The single-index model is an important tool in multivariate nonparamet- ric regression. Not only it can reduce the dimension of data and avoid the so-called ＂curse of dimensionality＂ in multivariate nonparametric regression, but also can cap- ture the main feature of high-dimensional data. This paper deals with M-estimatorfor the partial linear single-index model. An M-estimator procedure based on B-spline approximation is proposed in this paper. Under some mild regular conditions, the asymptotic properties of the proposed M-estimator of unknown function and the M- estimator of parameter are investigated. A finite sample simulation study indicates that the M-estimators proposed in this paper are robust.

关 键 词：部分线性单指标 M-估计 B-样条 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]