Sure Independence Screening (SIS) for Multiple Functional Regression Model

• Activity Number: 465 - SPEED: Statistical Computing: Methods, Implementation, and Application, Part 1
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Yuan Yuan* and Nedret Billor
• Companies: Auburn University and Auburn University
• Keywords: variable screening; variable selection ; Sure Independence Screening; functional data analysis

Abstract

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 etc. Variable selection has consequently become one of the most important problems in statistical research in recent years. We consider variable selection problem where variables are given as functional forms. Since functional data are inherently infinite dimensional, variable selection problem in multiple functional regression model is, therefore, challenging and difficult. In this study, we attempt to extend Sure Independence Screening (Fan and Lv, 2008) (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 screen out important functional predictors accurately and reduce dimensionality efficiently. Our methodology and theory are validated by simulation studies as well as some applications to data.