Time-Warping for Metric Space-Valued Random Processes

• Activity Number: 89 - Nonparametric Methods for Modern Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yaqing Chen * and Hans-Georg Müller
• Companies: University of California, Davis and University of California, Davis
• Keywords: Fréchet regression; functional data; mortality distributions; pairwise synchronization; phase variation; uniform convergence

Abstract

For real-valued functional data, it is well known that failure to separate amplitude variation from phase variation may contaminate subsequent statistical analysis and time warping methods to address this have been extensively investigated. However, much less is known about the phase variation problem for object-valued random processes that take values in a general metric space which by default does not have a linear structure. We introduce here a method to estimate warping functions by pairwise synchronization. An important starting point is uniform convergence of local Fréchet regression, which is a key result in its own right that we establish. We show how this result can be harnessed to obtain consistency and rates of convergence of the proposed warping function estimates. The proposed warping method is illustrated with mortality data consisting of yearly age-at-death distributions for different countries.