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Activity Number: 215 - Non- and Semiparametric Methods to Accommodate Dependency and Heterogeneity in Complex Data
Type: Invited
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #326513
Title: Nonparametric Modeling of Longitudinal Compositional Data as Trajectories on the Sphere
Author(s): Hans Mueller* and Xiongtao G Dai
Companies: UC Davis and University of California, Davis
Keywords: Functional Data Analysis; Riemannian Manifold; Principal Component Analysis; Central Limit Theorem; Rate of Convergence; Longitudinal Study

Longitudinal compositional data exhibit dependencies over time as well as among the p components of the compositional vectors, as these are constrained to be non-negative and to sum to 1. Such data are encountered in longitudinal modeling of behaviors for samples of individuals and in many other contexts, for example in metabolomics. This type of data can be represented as trajectories on the positive quadrant of a (p-1)-dimensional sphere. This motivates the study of functional data with trajectories on smooth Riemannian manifolds, with spheres as a special case. Of particular interest is the associated Riemannian functional principal component analysis. The proposed methods are supported by theory and will be illustrated with data from various application areas.

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

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