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Activity Number: 310 - Topics of Variable Selection
Type: Contributed
Date/Time: Tuesday, July 31, 2018 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #326987 Presentation
Title: Robust Group LASSO Methods
Author(s): Kristin Lilly* and Nedret Billor
Companies: Columbus State University and Auburn University
Keywords: Group LASSO; Robust Variable Selection ; Multiple regression; Group variable selection

Group variable selection is a relatively new problem in statistics. When the predictors can be naturally grouped in regression analysis, it is important to select important groups of variables that are influencing the response. One method of performing group variable selection is a method based on the least absolute shrinkage and selection operator (LASSO), which is called the group LASSO. This method works well in most cases, but has issues when there are outliers in the response. This paper proposes two methods which are based on the least absolute deviation (LAD), the group LAD-LASSO and the adaptive group LAD-LASSO, to perform group variable selection in the presence of outliers in the response. Both methods perform well when there are outliers in the y-direction; however, only the adaptive version has nice theoretical properties, including the oracle property. Further, selection of the shrinkage parameter and those properties are discussed. Simulation studies and an application to a real data set are also presented for both methods.

Authors who are presenting talks have a * after their name.

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