A0580
Title: Cross-component registration for multivariate functional data: Application to growth curves
Authors: Alois Kneip - University of Bonn (Germany) [presenting]
Cody Carroll - University of California Davis (United States)
Hans-Georg Mueller - University of California Davis (United States)
Abstract: Multivariate functional data are becoming ubiquitous with the advance of modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the component processes are subject to mutual time warping. That is, the component processes exhibit a similar shape but are subject to mutual time-warping across their domains. To address this previously unconsidered mode of warping, we propose a new registration methodology based on a shift-warping model. The method differs from all existing registration methods for functional data in a fundamental way. Namely, instead of focusing on the traditional approach to warping, where one aims to recover individual-specific registration, we focus on shift registration across the components of a multivariate functional data vector on a population-wide level. The proposed estimates for these shifts are identifiable, enjoy parametric rates of convergence and often have intuitive physical interpretations, all in contrast to traditional curve-specific registration approaches. We demonstrate the implementation and interpretation of the proposed method by applying our methodology to the Zuerich Longitudinal Growth data and study its finite sample properties in simulations.
