A robust sparse linear approach for contaminated data

Abstract

A challenging problem in a linear regression model is to select a parsimonious model which is robust to the presence of contamination in the data. In this paper, we present a sparse linear approach which detects outliers by using a highly robust regression method. The model with optimal predictive ability as measured by the median absolute deviation of the prediction errors on JackKnife subsets is used to detect outliers. The performance of the proposed method is evaluated on a simulation study with a different type of outliers and high leverage points and also on a real data set.

Keywords:

• JackKnife
• Outlier detection
• Robust variable selection
• Sparsity

Acknowledgments

The authors would like to thank to the Associate Editor and the reviewers for their useful comments which led to a considerable improvement of the manuscript. This work was supported by FEDER Funds through “Programa Operacional Factores de Competitividade-COMPETE” and by Portuguese Funds through FCT “Fundação para a Ciência e a Tecnologia”, within the SFRH/BD/51164/2010 and PEst-OE/MAT/UI0013/2017.

Notes

1 FAST-LTS algorithm (Rousseeuw and Van Driessen (2006)) was used inside the implementation of the proposed method.