310 – Topics of Variable Selection
Robust Group LASSO Methods
Kristin Lilly
Columbus State University
Nedret Billor
Auburn University
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.