A0459
Title: Additive regression with general imperfect variables
Authors: Jeong Min Jeon - Seoul National University (Korea, South) [presenting]
Germain Van Bever - Universite de Namur (Belgium)
Abstract: An additive model is introduced, 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, functional variables taking values in a Riemannian manifold and the case where only a random sample can be covered from a density-valued response is available. Dealing with imperfect predictors allows us to cover various principal component and singular component scores obtained from Hilbert-space-valued variables. The smooth back-fitting method is used to estimate the additive model having such variables. Asymptotic properties of the regression estimator are provided, and a numerical study is presented.
