空间非参回归的变量选择  

Variable selection for spatial nonparametric regression

作　　者：王康宁[1,2] 林路[2] 

机构地区：[1]重庆文理学院群与图的理论及应用研究重点实验室,重庆402160 [2]山东大学金融研究院,济南250100

出　　处：《中国科学：数学》2016年第3期301-320,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11171188和71271227);重庆高校创新团队建设计划(批准号:KJTD201321);重庆文理学院校级科研(批准号:Y2014SC35);重庆市教委科技(批准号:KJ1501109);全国统计科学研究(批准号:2014LY073)资助项目

摘　　要：空间变系数回归模型是空间线性回归模型的重要推广,在实际中有广泛的应用.然而,这个模型的变量选择问题还没有解决.本文通过一般的M型损失函数将均值回归、中位数回归、分位数回归和稳健均值回归纳入同一框架下,然后基于B样条近似,提出一个能够同时进行变量选择和函数系数估计的自适应组内(adaptive group)L_r(r≥1)范数惩罚的M型估计量.新方法有几个显著的特点:(1)对异常点和重尾分布稳健;(2)能够兼容异方差性,允许显著变量集合随所考虑的分位点不同而变化;(3)兼顾了估计量的有效性和稳健性.在较弱假设条件下,建立了变量选择的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现.Spatial varying coefficient regression model is an important generalization of spatial linear regression model. It is useful in real application. However, how to make variable selection for it has not been well studied.In this paper, a general M-type loss function is used to treat mean, median, quantile and robust mean regressions in one setting. Then by B-spline approximation, we propose an adaptive group L_r（r≥1） penalized M-type estimator, which can select relevant variables and estimate functional coefficients simultaneously. Moreover, it has several distinctive features：（1） It achieves robustness against outliers and heavy-tail distributions;（2） it is more flexible to accommodate heterogeneity and allows the set of relevant variables to vary across quantiles;（3）it can keep balance between efficiency and robustness. Under mild conditions, the oracle property is established.Simulation studies and real data analysis are conducted to assess the finite sample property of the proposed method.

关 键 词：空间数据 变量选择 稳健性 异方差 惩罚的M型估计 oracle性质 

分 类 号：O212.1[理学—概率论与数理统计]