Title: Additive regression for predictors of various natures and Hilbertian responses with application to censored/missing data
Authors: Byeong Park - Seoul National University (Korea, South) [presenting]
Ingrid Van Keilegom - KU Leuven (Belgium)
Jeong Min Jeon - Seoul National University (Korea, South)
Abstract: A fully nonparametric additive regression model for responses and predictors of various natures is considered. This includes the case of Hilbertian and incomplete responses (like censored or missing responses), and continuous, discrete or even nominal predictors. We propose a backfitting technique that estimates this additive model, and establish the existence of the estimator and the convergence of the associated backfitting algorithm under minimal conditions. We also develop a general asymptotic theory for the estimator, which includes even the case where there is no continuous predictor in the model. We verify the practical performance of the proposed estimator in an extensive simulation study, and apply the method to four data sets, containing respectively a missing scalar response, a censored scalar response, a compositional response and a functional response.