University of Notre Dame
Colloquium Tea held at 3:15 pm in 101A Crowley Hall
Title: On surrogate-assisted sufficient dimension reduction and variable selection for distributional responses
Abstract: There are many aspects of a distribution that are of interest. To this end, we propose a novel sufficient dimension reduction (SDR) method called surrogate-assisted SDR for regression with distributional responses. Surrogate-assisted SDR generalizes regression with random response objects in a bounded metric space, including scalars, positive definite matrices, and spheres. We first transform the response objects into a pairwise distance matrix using an appropriate metric. Then the central space for the regression between the distance matrix and the original predictor is estimated via an ensemble of scalar projections of the distance matrix using existing univariate response SDR methods. Surrogate-assisted SDR is applicable in numerous real data applications. It also aids in model-free variable selections. An extensive simulation study on synthetic data demonstrates the superior performance of the proposed surrogate-assisted SDR. We illustrate the usefulness of surrogate-assisted SDR with an analysis of the distributions of COVID-19 transmission in the United States as a function of county demographics.