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Activity Number: 582 - Statistical Methods for Functional Data
Type: Contributed
Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #323573
Title: Wasserstein Covariance for the Functional Data Analysis of Multivariate Densities
Author(s): Alexander Petersen* and Hans-Georg G Müller
Companies: University of California, Santa Barbara and University of California, Davis
Keywords: Functional Connectivity ; Random Densities ; Fréchet Mean ; Fréchet Variance ; Wasserstein Metric

While a variety of methods exist for analyzing samples of probability density functions, a common element in the majority of these is the incorporation of the constraints inherent to the space of densities. In the setting of one dimensional densities, the Wasserstein metric is popular due to its theoretical appeal and interpretive value, leading to the Wasserstein-Fréchet mean or barycenter. We extend the existing methodology for samples of densities in two important ways. First, motivated by applications in neuroimaging, we consider multivariate density data, where a vector of univariate random densities is observed for each sampling unit. Second, we define a novel population object, the Wasserstein covariance matrix. Intuitive estimators and their asymptotic performance are investigated while accounting for errors introduced by preliminary density estimation. The utility of the Wasserstein covariance matrix is demonstrated through the analysis of local functional connectivity distributions arising from fMRI data. In particular, Wasserstein covariance matrices at the individual level are shown to be intimately related to higher cognitive scores of episodic memory.

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

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