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MCD-RoSIS – A robust procedure for variable selection

Charlotte Guddat, Ursula Gather, and Sonja Kuhnt

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Consider the task of estimating a regression function for describing the relationship between a response and a vector of p predictors. Often only a small subset of all given candidate predictors actually effects the response, while the rest might inhibit the analysis. Procedures for variable selection aim to identify the true predictors. A method for variable selection when the dimension p of the regressor space is much larger than the sample size n is Sure Independence Screening (SIS). The number of predictors is to be reduced to a value less than the number of observations before conducting the regression analysis. As SIS is based on nonrobust estimators, outliers in the data might lead to the elimination of true predictors. Hence, a robustified version of SIS called RoSIS was proposed which is based on robust estimators. Here, we give a modification of RoSIS by using the MCD estimator in the new algorithm. The new procedure MCD-RoSIS leads to better results, especially under collinearity. In a simulation study we compare the performance of SIS, RoSIS and MCD-RoSIS w.r.t. their robustness against different types of data contamination as well as different degrees of collinearity.

Chapter information

J. Antoch, M. Hušková and P.K. Sen, eds., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 75-83

First available in Project Euclid: 29 November 2010

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Mathematical Reviews number (MathSciNet)

Primary: 62G35: Robustness 62J99: None of the above, but in this section

Variable selections dimension reduction regression outliers robust estimation

Copyright © 2010, Institute of Mathematical Statistics


Guddat, Charlotte; Gather, Ursula; Kuhnt, Sonja. MCD-RoSIS – A robust procedure for variable selection. Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, 75--83, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL708.

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