Deleting Outliers in Robust Regression with Mixed Integer Programming  

作　　者：Georgios Zioutas Antonios Avramidis 

机构地区：[1]Division of Computational Methods and Computer Programming, General Department, Faculty of Technology, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece,Division of Computational Methods and Computer Programming, General Department, Faculty of Technology, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece

出　　处：《Acta Mathematicae Applicatae Sinica》2005年第2期323-334,共12页应用数学学报（英文版）

摘　　要：In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.

关 键 词：Robust regression quadratic mixed integer programming least trimmedsquares deleting outliers penalty methods 

分 类 号：O221.4[理学—运筹学与控制论]