Additive isotone regression

Abstract

This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymp-totically up to first order, each additive component can be estimated as well as it could be by a least squares estimator if the other components were known. The algorithm for the calculation of the estimator uses backfitting. Conver-gence of the algorithm is shown. Finite sample properties are also compared through simulation experiments.