Orthogonalizing EM: A Design-Based Least Squares Algorithm
文献类型：期刊论文
| 作者 | Xiong, Shifeng1 ; Dai, Bin2; Huling, Jared3; Qian, Peter Z. G.3
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| 刊名 | TECHNOMETRICS
 |
| 出版日期 | 2016-08-01 |
| 卷号 | 58期号:3页码:285-293 |
| 关键词 | Computational statistics Design of experiments Missing data Orthogonal design SCAD The Lasso |
| ISSN号 | 0040-1706 |
| DOI | 10.1080/00401706.2015.1054436 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[11271355] ; National Natural Science Foundation of China[11471172] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000381014100002 |
| 出版者 | AMER STATISTICAL ASSOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/23289]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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