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Activity Number: 243 - Functional Object Analysis and Beyond
Type: Contributed
Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #304854 Presentation
Title: Wasserstein F-Tests and Confidence Bands for the Fréchet Regression of Density Response Curves
Author(s): Alexander Petersen* and Xi Liu and Afshin Divani
Companies: University of California, Santa Barbara and University of California, Santa Barbara and University of Minnesota
Keywords: Random Densities; Least Squares Regression; Wasserstein Metric; Tests for Regression Effects; Simultaneous Confidence Band

Data consisting of samples of probability density functions necessitate the development of methodologies that respect the inherent nonlinearities associated with densities. In many applications, density curves appear as functional response objects in a regression model with vector predictors. For such models, inference is key to understand the importance of density-predictor relationships, and the uncertainty associated with the estimated conditional mean densities, defined as conditional Fréchet means under a suitable metric. Using the Wasserstein geometry of optimal transport, we consider the Fréchet regression of density response curves and develop tests for covariate effects and simultaneous confidence bands for estimated conditional mean densities. The asymptotic behavior of these objects is based on underlying functional central limit theorems within Wasserstein space, and we demonstrate that they are asymptotically of the correct size and coverage, with uniformly strong consistency of the proposed tests under sequences of contiguous alternatives. These methods are illustrated through a regression analysis of post-intracerebral hemorrhage hematoma densities.

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

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