PENALIZED TRIMMED SQUARES AND A MODIFICATION OF SUPPORTVECTORS FOR UNMASKING OUTLIERS IN LINEARREGRESSION英文电子书.pdf

REVSTAT – Statistical Journal Volume 5, Number 1, March 2007, 115–136 PENALIZED TRIMMED SQUARES AND A MODI- FICATION OF SUPPORT VECTORS FOR UN- MASKING OUTLIERS IN LINEAR REGRESSION ∗ Authors: G. Zioutas – General Department, Faculty of Technology, Aristotle University of Thessaloniki, Greece zioutas@eng.auth.gr A. Avramidis – General Department, Faculty of Technology, Aristotle University of Thessaloniki, Greece L. Pitsoulis – General Department, Faculty of Technology, Aristotle University of Thessaloniki, Greece Abstract: • We consider the problem of identifying multiple outliers in linear regression models. We propose a penalized trimmed squares (PTS) estimator, where penalty costs for discarding outliers are inserted into the loss function. We propose suitable penalties for unmasking the multiple high-leverage outliers. The robust procedure is formu- lated as a Quadratic Mixed Integer Programming (QMIP) problem, computationally suitable for small sample data. The computational load and the effectiveness of the new procedure are improved by using the idea of ǫ-insensitive loss function from sup- port vector machines regression. The small errors are ignored, and the mathematical formula gains the sparseness property. The good performance of the PTS estimator allows identification of multiple outliers avoiding masking effects. Key-Words: • robust regression; mixed integer programming; penalty method; least trimmed squares; identifying outliers; support vector machines. AMS Subject Classification: • 62F35, 62J99, 90C99. ∗This research has been partially funded by the Greek Ministry of Education under the program Pythagoras II. 116