标题：Variable selection and parameter estimation for partially linear models via Dantzig selector
作者：Li, F.;Lin, L.;Su, Y.
作者机构：[Li, F] Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou, China;[ Lin, L] School of Mathematics, Shandong University, Jinan, China;[ 更多
通讯作者地址：[Li, F]Zhengzhou Inst Aeronaut Ind Management, Zhengzhou, Peoples R China.
来源：Metrika: International Journal for Theoretical and Applied Statistics
关键词：Dantzig selector;DASSO;Partially linear models;Variable selection
摘要：Variable selection plays an important role in the high dimensionality data analysis, the Dantzig selector performs variable selection and model fitting for linear and generalized linear models. In this paper we focus on variable selection and parametric estimation for partially linear models via the Dantzig selector. Large sample asymptotic properties of the Dantzig selector estimator are studied when sample size n tends to infinity while p is fixed. We see that the Dantzig selector might not be consistent. To remedy this drawback, we take the adaptive Dantzig selector motivated by Dicker and Lin (submitted). Moreover, we obtain that the adaptive Dantzig selector estimator for the parametric component of partially linear models has the oracle properties under some appropriate conditions. As generalizations of the Dantzig selector, both the adaptive Dantzig selector and the Dantzig selector optimization can be implemented by the efficient algorithm DASSO proposed by James et al. (J R Stat Soc Ser B 71:127-142, 2009). Choices of tuning parameter and bandwidth are also discussed.