The Functional Linear Array Model

• Activity Number: 162
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sonja Greven*+ and Sarah Brockhaus and Fabian Scheipl and Torsten Hothorn
• Companies: LMU Munich and Ludwig Maximilians University and and University of Zurich
• Keywords: boosting ; functional data analysis ; functional linear model ; generalized functional data

Abstract

The Functional Linear Array Model (FLAM) is a unified model class for functional regression models including function-on-scalar, scalar-on-function and function-on-function regression. Within the general framework mean, median, quantile and generalized linear regression models for functional or scalar responses are contained as special cases. Covariate effects can be quite general and our current implementation supports linear, smooth and interaction effects of grouping variables, scalar and functional covariates. Computational efficiency is achieved by representing the model as a generalized linear array model (Currie et al. 2006). While the array structure requires a single grid for all responses, missing values are allowed. Estimation is conducted using a boosting algorithm, which allows for numerous covariates and model selection. To illustrate the flexibility of the model class we use three applications requiring functional responses and/or covariates as well as additional capabilities such as robust regression, spatial functional regression, model selection and accommodation of missings. An implementation of our methods is provided in the R add-on package FDboost on R-Forge.