Variable Selection in Fully Functional Regression Models

• Activity Number: 286
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Alexander Aue* and Holger Dette and Siegfried Hörmann
• Companies: UC Davis and Ruhr University Bochum and Université libre de Bruxelles
• Keywords: Dimension reduction ; Functional data analysis ; Functional principal components

Abstract

This talk discusses new variable selection methodology for fully functional regression models. While variants of the LASSO regularization techniques have been introduced to select significant predictors in functional regression with scalar responses, most articles dealing with fully functional regressions have incorporated only a single predictor, and possibly its derivatives, into the model building process. To the best of our knowledge, no variable selection methods are currently available in the literature for this case. The methodology proposed, then, seeks to select significant functional predictors for functional responses by obtaining an auxiliary multivariate linear model of functional principal component scores. The significant predictors as well as the dimensionality of both response and predictor score vectors are determined through a novel automatic penalization criterion. Theoretical and empirical results justify the use of the new methodology.