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Activity Number: 614 - Statistical Methods for Longitudinal and Other Dependent Data
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #306798
Title: Statistical Analysis of Longitudinal Data on Riemannian Manifolds
Author(s): Xiongtao Dai* and Zhenhua Lin and Hans Mueller
Companies: Iowa State University and University of California, Davis and UC Davis
Keywords: Functional Data; PACE; Imputation; Nonparametrics; Smoothing; Connectivity

A manifold version of the principal analysis by conditional expectation (PACE) is proposed to represent sparsely observed longitudinal data that take values on a nonlinear Riemannian manifold. Typical examples of such manifold-valued data include longitudinal compositional data and shapes. Compared to standard functional principal component analysis that is geared towards Euclidean geometry, the proposed approach leads to improved trajectory recovery on nonlinear manifolds in simulations. The proposed method is illustrated with the longitudinal emotional well-being data of unemployed workers modeled as compositional data, and is applicable to model the development of neuroconnectivity as covariance matrices. An R implementation of our method is available on GitHub.

Authors who are presenting talks have a * after their name.

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