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Orthogonalizing EM: A Design-Based Least Squares Algorithm
| Content Provider | Scilit |
|---|---|
| Author | Xiong, Shifeng Dai, Bin Huling, Jared Qian, Peter Z. G. |
| Copyright Year | 2016 |
| Description | Journal: Technometrics 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. |
| Related Links | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4974022/pdf |
| Ending Page | 293 |
| Page Count | 9 |
| Starting Page | 285 |
| ISSN | 00401706 |
| e-ISSN | 15372723 |
| DOI | 10.1080/00401706.2015.1054436 |
| Journal | Technometrics |
| Issue Number | 3 |
| Volume Number | 58 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2016-07-02 |
| Access Restriction | Open |
| Subject Keyword | Journal: Technometrics Statistics and Probability Design of Experiments Computational Statistics Missing Data Optimization Orthogonal Design |
| Content Type | Text |
| Subject | Applied Mathematics Statistics and Probability Modeling and Simulation |
