桥回归的系数估计对应于γ-范数的压缩规律.pdfVIP

应用概率统计 第三十一卷 Chinese Journal of Applied Probability 第四期 2015年8月 and Statistics Vol.31 No .4 Aug. 2015 General Shrinkage Rule with Respect to 千Norms for Bridge Estimation * GAI YUJIE ZHANG ZHANLI (Sch阳ool们of 8;ωisticωsα叫Maωthemα阳， Cenηltral u:阳阳倪仰er内sit句，y of Finance and Econom阳比 B叫呻咿j纠仰tr叼 100081) ZHANG JUN食 (Shen Zhen 一 Ho叼Ko叼 Joint Resea时Centre for Applied Statistical S优， nc矶 College 01 Mathematics and Computational Science , Institute of Statistical Sciences, Shenzhen University, Sher圳矶 5180ω) Abstract Bridge regression , a special family of penalized regr岱sions of a penalty function 艺Ißj 尸 with γ 0 , h副 been studied in many literatures. In this paper , we provide some theoretical results of how the shrinkage rule changing with γunder two settings:γ 2: 1 and 0 γ 1, respectively. Simulation results 缸e conducted to evaluate the performance of the proposed method. Keywords: Bridge estimation , high-dimensional linear model , variable selection, shrinkage rule. AMS Subject Classification: 62F12 , 62G05 , 62G08. ~1. Introduction Consider the linear model Ei=z;β:0+ 句， í = 1, 2,..., n , (1. 1) where yi ε 1R1 is a response variable , Xi ξ W is a p x 1 covarÍate vector , and the 句s 町e i.i.d. mode1 errors. Without 10ss