In this talk we present a new method of linear regression using Hilbert-space valued covariates with unknown reproducing kernels. We develop a computationally efficient approach to estimation and derive asymptotic theory for the regression parameter estimates under mild assumptions. We demonstrate the approach in simulation studies as well as in a data analyses using two- and three-dimensional brain images as predictors. The is work is a collaboration with Xinyi Li and Margaret Hoch.

Short Bio: Michael R. Kosorok, PhD, is the W.R. Kenan, Jr. Distinguished Professor of Biostatistics, Professor of Statistics and Operations Research, and Director of the Center for Artificial Intelligence and Public Health at the University of North Carolina at Chapel Hill. His interests include biostatistics, artificial intelligence, empirical processes, and precision health. He is a fellow of the ASA, IMS and AAAS, and is past-president of IMS.