MCD-RoSIS - A robust procedure for variable selection
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Date
2010-02-08T14:40:40Z
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Abstract
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 SIS — Sure Independence Screening — recently proposed by Fan and Lv (2008).
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, Gather and Guddat (2008) propose a robustified version of SIS called RoSIS 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.
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Keywords
Dimension reduction, Outlier, Regression, Robust estimation, Variable selection