 Outlier detection and least trimmed squares approximation using semi-definite programmingT.D. Nguyen and R. Welsch Computational Statistics & Data Analysis, 2010, vol. 54, issue 12, 3212-3226 Abstract: Robust linear regression is one of the most popular problems in the robust statistics community. It is often conducted via least trimmed squares, which minimizes the sum of the k smallest squared residuals. Least trimmed squares has desirable properties and forms the basis on which several recent robust methods are built, but is very computationally expensive due to its combinatorial nature. It is proven that the least trimmed squares problem is equivalent to a concave minimization problem under a simple linear constraint set. The "maximum trimmed squares", an "almost complementary" problem which maximizes the sum of the q smallest squared residuals, in direct pursuit of the set of outliers rather than the set of clean points, is introduced. Maximum trimmed squares (MTS) can be formulated as a semi-definite programming problem, which can be solved efficiently in polynomial time using interior point methods. In addition, under reasonable assumptions, the maximum trimmed squares problem is guaranteed to identify outliers, no mater how extreme they are. Date: 2010 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:54:y:2010:i:12:p:3212-3226 Access Statistics for this article Computational Statistics & Data Analysis is currently edited by S.P. Azen More articles in Computational Statistics & Data Analysis from Elsevier |
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