Additive isotone regression

TL;DR

This paper introduces an optimal estimation method for additive isotone regression components, demonstrating asymptotic efficiency, algorithm convergence, and finite sample performance through simulations.

Contribution

It develops a backfitting algorithm for additive isotone regression and proves its asymptotic optimality and convergence.

Findings

Asymptotic estimation matches the best possible if other components are known.

The backfitting algorithm converges.

Finite sample properties are validated via simulations.

Abstract

This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically 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. Convergence of the algorithm is shown. Finite sample properties are also compared through simulation experiments.