Modeling Time-Varying Object Data

• Activity Number: 133 - Statistical Methods for Functional Data
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Paromita Dubey* and Hans Mueller
• Companies: University of California, Davis and UC Davis
• Keywords: Frechet mean trajectory; Functional data analysis; Object time courses; Random objects; Time varying distributions; Time varying networks

Abstract

Time-varying object data are increasingly encountered in modern data analysis. Functional data analysis is often used for analyzing Euclidean time-varying data, but is infeasible for time courses of non-Euclidean data taking values in metric spaces rather than vector spaces. We propose a generalized notion of mean trajectory by using Frechet means and consider pointwise distance trajectories between the individual time courses and the estimated Frechet mean trajectory. Functional principal component analysis of these distance trajectories leads to better understanding of the object time courses and can be used for clustering, classification as well as detection of outliers in a sample of object trajectories. Functional data tools are not directly applicable as the estimated distance trajectories are not independent. We define suitable population targets and show desirable asymptotic properties of the corresponding estimators. We illustrate our approach with time-varying maternal age distributions of various countries from 1976 to 2009, time-varying daily networks of taxi trips between 69 zones in Manhattan in 2016 and evolving trade networks between 61 countries from 1970 to 2000.