Laplace Error Penalty-based Variable Selection in High Dimension

doi:10.1111/sjos.12130

CORC > 上海财经大学 > 上海财经大学

	Laplace Error Penalty-based Variable Selection in High Dimension
	Wen, Canhong 1,2; Wang, Xueqin 3,4; Wang, Shaoli 5
刊名	SCANDINAVIAN JOURNAL OF STATISTICS
	2015-09
卷号	42 期号:3 页码:685-700
关键词	coordinate descent majorization minimization high-dimensional regression Laplace error penalty oracle property smooth penalty function sparsity variable selection
ISSN号	0303-6898
DOI	10.1111/sjos.12130
英文摘要	We propose the Laplace Error Penalty (LEP) function for variable selection in high-dimensional regression. Unlike penalty functions using piecewise splines construction, the LEP is constructed as an exponential function with two tuning parameters and is infinitely differentiable everywhere except at the origin. With this construction, the LEP-based procedure acquires extra flexibility in variable selection, admits a unified derivative formula in optimization and is able to approximate the L-0 penalty as close as possible. We show that the LEP procedure can identify relevant predictors in exponentially high-dimensional regression with normal errors. We also establish the oracle property for the LEP estimator. Although not being convex, the LEP yields a convex penalized least squares function under mild conditions if p is no greater than n. A coordinate descent majorization-minimization algorithm is introduced to implement the LEP procedure. In simulations and a real data analysis, the LEP methodology performs favorably among competitive procedures.
WOS研究方向	Mathematics
语种	英语
出版者	WILEY-BLACKWELL
WOS记录号	WOS:000360077100003
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/1488]
专题	上海财经大学
通讯作者	Wang, Shaoli
作者单位	1.Sun Yat Sen Univ, Southern China Res Ctr Stat Sci, Guangzhou, Guangdong, Peoples R China; 2.Sun Yat Sen Univ, Dept Stat Sci, Sch Math & Computat Sci, Guangzhou, Guangdong, Peoples R China; 3.Sun Yat Sen Univ, Dept Stat Sci, Sch Math & Computat Sci, Southern China Res Ctr Stat Sci, Guangzhou, Guangdong, Peoples R China; 4.Sun Yat Sen Univ, Zhongshan Sch Med, Guangzhou, Guangdong, Peoples R China; 5.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Wen, Canhong,Wang, Xueqin,Wang, Shaoli. Laplace Error Penalty-based Variable Selection in High Dimension[J]. SCANDINAVIAN JOURNAL OF STATISTICS,2015,42(3):685-700.
APA	Wen, Canhong,Wang, Xueqin,&Wang, Shaoli.(2015).Laplace Error Penalty-based Variable Selection in High Dimension.SCANDINAVIAN JOURNAL OF STATISTICS,42(3),685-700.
MLA	Wen, Canhong,et al."Laplace Error Penalty-based Variable Selection in High Dimension".SCANDINAVIAN JOURNAL OF STATISTICS 42.3(2015):685-700.