Session: Alumni Session

Date & Time: Saturday, May 23 — 1:30 PM–3:00 PM

Talk Title

Modeling Amplitude and Phase Variation of Multivariate Random Processes in Metric Spaces

Abstract

In functional data analysis, distinguishing between amplitude and phase variation is essential to prevent distorted statistical inferences. While extensive work has been devoted to developing time-warping methods to address this issue for Euclidean functional data, much less is known about how to characterize and model these two sources of variability when they co-exist in random processes taking values in general metric spaces. In this work, we develop a comprehensive statistical framework characterizing amplitude and phase variation for multivariate metric-space-valued functional data. We propose a geodesic latent deformation model (GLDM) for jointly analyzing both types of variation by using tools from metric geometry, and define tempo indices to quantify the temporal dynamics. We devise a novel estimation procedure and establish (uniform) convergence rates for the model estimators. The method's broad applicability is demonstrated through a real-world application to annual gender-specific age-at-death distributions providing new insights into global longevity dynamics as well as simulations on multivariate positive semi-definite (PSD) matrix-valued and network-valued functional data.