Robust Adaptive Functional Mixed Models for Correlated Functional Data

• Activity Number: 406
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Hongxiao Zhu*+ and Jeffrey S. Morris
• Companies: Virginia Tech and The University of Texas MD Anderson Cancer Center
• Keywords: Bayesian methods ; Adaptive LASSO ; Correlated Functional Data ; Functional Data Analysis ; Mixed Models ; Variable Selection

Abstract

Robust functional mixed model (R-FMM) is a flexible framework recently proposed to model functional data that are influenced by outliers and various random effects caused by complex experimental design. It has several nice properties such as robust estimation, adaptive smoothing and false-discovery-rate based region selection. Although R-FMM can accommodate correlations induced by grouping, it is not clear how it can take into account correlations induced by longitudinal or spatial measurements. Typical examples include fMRI measurements or EEG data. In this talk, I will show how R-FMM can be extended to accommodate functional data with longitudinally or spatially correlations. Such correlations were modeled through introducing several types of correlation structures, such as AR(1), Matern to the residuals in the wavelet domain. We show the performance of the method through simulation studies and an fMRI application.