A0890
Title: Regression modeling for distributional response data
Authors: Alexander Petersen - Brigham Young University (United States) [presenting]
Wendy Meiring - University of California Santa Barbara (United States)
Xi Liu - University of California Santa Barbara (United States)
Aritra Ghosal - University of California Santa Barbara (United States)
Abstract: Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis 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. We consider two such models in which the regression function takes the form of conditional Fr\'echet means under the Wasserstein geometry of optimal transport. The first model, known as global Fr\'echet regression, is developed as a generalization of multiple linear regression, for which we demonstrate the use of hypothesis testing of global and partial effects, as well as simultaneous confidence bands for estimated conditional mean densities. In the second, greater flexibility in the predictor-response relationship is achieved by a generalization of single-index models, fitted by local Fr\'echet regression techniques. These methods are illustrated through regression analyses of post-intracerebral hemorrhage hematoma densities and distributions of age-at-death for various countries.
