KMS Of Academy of mathematics and systems sciences, CAS
Orthogonalizing EM: A Design-Based Least Squares Algorithm | |
Xiong, Shifeng1; Dai, Bin2; Huling, Jared3; Qian, Peter Z. G.3 | |
2016-08-01 | |
Source Publication | TECHNOMETRICS |
ISSN | 0040-1706 |
Volume | 58Issue:3Pages:285-293 |
Abstract | 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. |
Keyword | Computational statistics Design of experiments Missing data Orthogonal design SCAD The Lasso |
DOI | 10.1080/00401706.2015.1054436 |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11271355] ; National Natural Science Foundation of China[11471172] |
WOS Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000381014100002 |
Publisher | AMER STATISTICAL ASSOC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/23290 |
Collection | 系统科学研究所 |
Affiliation | 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 |
Recommended Citation 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. |
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