Additive regression for Riemannian functional responses

Abstract

We explore additive regression for a functional response whose values lie on a general Riemannian manifold. Due to the absence of a vector space structure on the manifold, we transform the response into a vector space. The transformation involves an unknown quantity that needs to be estimated. An additive model on the vector space is estimated using the smooth backfitting method, which effectively avoids the curse of dimensionality. We derive its rates of convergence and demonstrate its practical performance through a simulation study and a real data application.