Non-convex penalized estimation in high-dimensional models with single-index structure

被引:35
作者
Wang, Tao
Xu, Pei-Rong
Zhu, Li-Xing [1 ]
机构
[1] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
关键词
High-dimensional variable selection; Minimax concave penalty; Oracle property; Penalized least squares; SCAD; Single-index model; INVERSE REGRESSION; VARIABLE SELECTION; DIVERGING NUMBER; REDUCTION; LASSO; LIKELIHOOD; SHRINKAGE; ALGORITHM;
D O I
10.1016/j.jmva.2012.03.009
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
As promising alternatives to the LASSO, non-convex penalized methods, such as the SCAD and the minimax concave penalty method, produce asymptotically unbiased shrinkage estimates. By adopting non-convex penalties, in this paper we investigate uniformly variable selection and shrinkage estimation for several parametric and semi-parametric models with single-index structure. The new method does not need to estimate the involved nonparametric transformation or link function. The resulting estimators enjoy the oracle property even in the "large p, small n" scenario. The theoretical results for linear models are in parallel extended to general single-index models with no distribution constraint for the error at the cost of mild conditions on the predictors. Simulation studies are carried out to examine the performance of the proposed method and a real data analysis is also presented for illustration. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码:221 / 235
页数:15
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