Jin-Ting Zhang (Chair)

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 class of such object data are univariate probability measures and associated regression problems are of broad interest.  A recent approach is Wasserstein regression that utilizes tangent bundles of the Wasserstein metric space.  The search for an intrinsic method motivated a novel transport algebra in the space of optimal transports, which can be harnessed for transport based distributional regression. This approach is illustrated with an autoregressive optimal transport model for distributional time series. (Joint work with Changbo Zhu, Notre Dame University)