RSFAS Seminar Series – Professor Hans-Georg Müller

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Speaker: Professor Hans-Georg Müller

Institution: University of California, Davis

Title: Wasserstein Regression for Distributions and Distributional Time Series

Abstract: The analysis of samples of random objects that do not lie in a vector space has found increasing attention in statistics in recent years. An important setting for distributional data analysis are samples consisting of univariate probability measures defined on the real line. Adopting the Wasserstein-2  metric, we propose a class of regression models for such data, where random distributions serve as predictors and the responses are either also distributions or scalars. To define this regression model, we utilize the geometry of tangent bundles of the metric space of random measures with the Wasserstein metric. The proposed distribution-to-distribution regression model provides an extension of classical linear regression to the case of distributional data. We study asymptotic rates of convergence for the estimator of the regression coefficient function and for predicted distributions. Extensions include autoregressive modeling of  distribution-valued time series and an intrinsic  optimal transport regression model.  The proposed methods are illustrated with data on human mortality and other distributional data. This talk is based on joint work with Yaqing Chen (Davis), Zhenhua Lin (Singapore) and Changbo Zhu (Davis). 

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