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Contributed Presentations

Robust Sparse Functional Regression Model (309983)

*Jasdeep Pannu, California State University, Sacramento 

Keywords: Functional Outliers, WLAD, LASSO

The objective of this study is to propose a robust variable selection technique for the functional variables using L1 regularization in a functional linear regression model with a scalar response and functional predictors in the presence of outliers. Recently, a method called robust functional group LASSO [4] has been developed which uses the combination of the well known robust loss function least absolute deviation (LAD) and penalty function group LASSO, where the functional parameters are estimated and selected through the minimization of the sum of the absolute value of the errors and penalizing the parameter functions. However, it is well known that the LAD based method is only resistant to the outlier in the response variable, but not resistant to the outliers in the explanatory variables (leverage points). To address this issue we propose a new method called functional Weighted LAD-Adaptive group LASSO (WLAD-agLASSO). This method is not only resistant to outliers in the response variable but also minimizes the effect of the leverage points by introducing weights which are only dependent on the functional predictors. This method uses WLAD function to downweight the leverage points and Adaptive groupLASSO penalty criterion to assign different weights to different coefficients to penalize them differently.