Permutation Tests for Comparison of Covariance Operators

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Davide Pigoli*+ and John Aston and Ian L. Dryden and Piercesare Secchi
• Companies: University of Warwick and University of Warwick and University of Nottingham and Politecnico di Milano
• Keywords: Functional data analysis ; Non parametric methods ; Metrics for covariance operators

Abstract

Data sets are increasingly becoming available that are best described as being functional. Here, the focus is on the comparison between different populations of functional data focusing on their covariance operators. In this context, the need is for a procedure with good finite sample properties in the non Gaussian case, thus we propose a non parametric approach, namely permutation tests. We show that a crucial point in the procedure is to choose the correct metric for evaluating the difference between sample covariance operators. While some distances defined for finite dimensional covariance matrices naturally lend themselves to functional analogues, others do not have natural extensions. It will be shown that the metrics can be intuitively understood as looking at different properties of the underlying covariance structure. The performances of the different metrics in the proposed method are evaluated by means of simulation studies. Finally, the testing procedure is applied in a study into cerebral aneurysms, where it is necessary to investigate the difference in covariance structures of radius and curvature of Internal Carotid Artery between different groups of patients.