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A fast algorithm for robust regression with penalised trimmed squares

Content Provider	Springer Nature Link
Author	Pitsoulis, L. Zioutas, G.
Copyright Year	2010
Abstract	The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in Zioutas and Avramidis (2005) Acta Math Appl Sin 21:323–334, Zioutas et al. (2007) REVSTAT 5:115–136 and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.
Starting Page	663
Ending Page	689
Page Count	27
File Format	PDF
ISSN	09434062
Journal	Computational Statistics
Volume Number	25
Issue Number	4
e-ISSN	16139658
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-04-11
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Robust regression Quadratic mixed integer programming Least trimmed squares Outliers detection Economic Theory Probability Theory and Stochastic Processes Probability and Statistics in Computer Science Statistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty Computational Mathematics

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