Special Colloquium
Kyunghee Han
University of Pennsylvania
Additive Functional Regression for Densities as Responses
Abstract: Distributions or densities are commonly encountered as functional outcomes un-
der shape constraints, which are monotone or non-negative. Examples include age
distributions for calendar years, survival functions for different countries, and gene
expression curves from microarray experiments. In such applications, functional re-
gression models associating covariates with distributions or densities are modeling
problems that incorporate geometry, inherent to the space of distribution or density
functions, into the regression analysis. In this talk, I will present the nonparamet-
ric estimation of additive functional regression models for distributions or densities
as responses, given multiple covariates. Additive modeling is attractive and widely
applicable for practical situations where dimensions of covariates are large since the
estimation of unstructured models is subject to the curse of dimensionality. Extend-
ing the Fr ́echet mean with the Wasserstein metric, I will introduce a smooth back-
fitting algorithm for estimating the proposed additive functional regression models
and establish the consistency of the back-fitting estimator, including the rate of
convergence.
Friday January 17, 2020 at 3:00 PM in 636 SEO