A0245
Title: Additive regression with general imperfect variables
Authors: Germain Van Bever - Universite de Namur (Belgium) [presenting]
Jeong Min Jeon - Seoul National University (Korea, South)
Abstract: An additive model is presented where the response variable is Hilbert-space-valued, and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows us to cover Euclidean, compositional, functional and density-valued variables. By treating imperfect responses, we can cover functional variables taking values in a Riemannian manifold and the case where only a random sample from a density-valued response is available. This treatment can also be applied in semiparametric regression. Dealing with imperfect predictors allows us to cover various principal component and singular component scores obtained from Hilbert-space-valued variables. For the estimation of the additive model having such variables, we use the smooth backfitting method. We provide full non-asymptotic and asymptotic properties of our regression estimator and present its wide applications via several simulation studies and real data applications.
