Sure independent screening for functional regression model

Due to rapid advancements in computer technology, high-dimensional, big, and complex data, such as functional data, where observations are considered as curves, have emerged from many applications in various disciplines of sciences, such as biomedicine, chemometrics, engineering, and social sciences. Variable selection has consequently become one of the most important problems in statistical research in recent years. As the functional data are inherently infinite dimensional, variable selection problem in multiple functional regression model is, therefore, challenging and difficult. In this study, we extend Sure Independence Screening (SIS) method to a multiple functional regression model with a scalar response and functional predictors. We show that the SIS-based procedure for multiple functional regression model retaining important functional predictors while screening out unimportant functional predictors, and reduce the dimension efficiently. Our methodologies are validated by simulation studies as well as some applications to data.