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March 2013 Robust VIF regression with application to variable selection in large data sets
Debbie J. Dupuis, Maria-Pia Victoria-Feser
Ann. Appl. Stat. 7(1): 319-341 (March 2013). DOI: 10.1214/12-AOAS584

Abstract

The sophisticated and automated means of data collection used by an increasing number of institutions and companies leads to extremely large data sets. Subset selection in regression is essential when a huge number of covariates can potentially explain a response variable of interest. The recent statistical literature has seen an emergence of new selection methods that provide some type of compromise between implementation (computational speed) and statistical optimality (e.g., prediction error minimization). Global methods such as Mallows’ $C_{p}$ have been supplanted by sequential methods such as stepwise regression. More recently, streamwise regression, faster than the former, has emerged. A recently proposed streamwise regression approach based on the variance inflation factor (VIF) is promising, but its least-squares based implementation makes it susceptible to the outliers inevitable in such large data sets. This lack of robustness can lead to poor and suboptimal feature selection. In our case, we seek to predict an individual’s educational attainment using economic and demographic variables. We show how classical VIF performs this task poorly and a robust procedure is necessary for policy makers. This article proposes a robust VIF regression, based on fast robust estimators, that inherits all the good properties of classical VIF in the absence of outliers, but also continues to perform well in their presence where the classical approach fails.

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Debbie J. Dupuis. Maria-Pia Victoria-Feser. "Robust VIF regression with application to variable selection in large data sets." Ann. Appl. Stat. 7 (1) 319 - 341, March 2013. https://doi.org/10.1214/12-AOAS584

Information

Published: March 2013
First available in Project Euclid: 9 April 2013

zbMATH: 06171274
MathSciNet: MR3086421
Digital Object Identifier: 10.1214/12-AOAS584

Keywords: $M$-estimator , college data , Linear regression , multicollinearity , Variable selection

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 1 • March 2013
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