M-estimators for Isotonic Regression

TL;DR

This paper introduces a family of robust isotonic M-estimators that maintain efficiency under Gaussian errors while providing robustness against heavy-tailed distributions, with theoretical and empirical validation.

Contribution

It proposes a new family of isotonic M-estimators with proven asymptotic properties, influence functions, and breakdown points, enhancing robustness in isotonic regression.

Findings

Estimators have asymptotic distribution similar to classical isotonic estimator.

The family includes estimators that are both efficient and robust.

Monte Carlo results confirm robustness and efficiency balance.

Abstract

In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk's classical isotonic estimator. We also derive the influence function and the breakdown point of these estimates. Finally we perform a Monte Carlo study that shows that the proposed family includes estimators that are simultaneously highly efficient under gaussian errors and highly robust when the error distribution has heavy tails.