Orthogonalizing EM: A Design-Based Least Squares Algorithm

doi:10.1080/00401706.2015.1054436

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	Orthogonalizing EM: A Design-Based Least Squares Algorithm
	Xiong, Shifeng1 ; Dai, Bin 2; Huling, Jared 3; Qian, Peter Z. G.3
	2016-08-01
发表期刊	TECHNOMETRICS
ISSN	0040-1706
卷号	58 期号:3 页码:285-293
摘要	We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares (OLS) and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the OLS with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online.
关键词	Computational statistics Design of experiments Missing data Orthogonal design SCAD The Lasso
DOI	10.1080/00401706.2015.1054436
语种	英语
资助项目	National Natural Science Foundation of China[11271355] ; National Natural Science Foundation of China[11471172]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000381014100002
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23290
专题	系统科学研究所
通讯作者	Xiong, Shifeng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Tower Res Capital, 377 Broadway, New York, NY 10013 USA 3.Univ Wisconsin, Dept Stat, Madison, WI 53706 USA
推荐引用方式 GB/T 7714	Xiong, Shifeng,Dai, Bin,Huling, Jared,et al. Orthogonalizing EM: A Design-Based Least Squares Algorithm[J]. TECHNOMETRICS,2016,58(3):285-293.
APA	Xiong, Shifeng,Dai, Bin,Huling, Jared,&Qian, Peter Z. G..(2016).Orthogonalizing EM: A Design-Based Least Squares Algorithm.TECHNOMETRICS,58(3),285-293.
MLA	Xiong, Shifeng,et al."Orthogonalizing EM: A Design-Based Least Squares Algorithm".TECHNOMETRICS 58.3(2016):285-293.