Robust sparse functional regression model

The presence of outliers, in general, affects the performance of the conventional statistical methods which require the homogeneity of observations. In this study, we consider variable selection problem in a functional regression model when a functional dataset contains outliers. We propose a functional adaptive group LASSO variable selection method based on the weighted least absolute deviation which takes into account the effect of outliers in bothxandydirections for a functional regression model with a scalar response and multiple functional predictors. Further, we demonstrate, through simulated and real datasets, that the proposed methods perform well.