On convex regression estimators

TL;DR

This paper introduces a new nonparametric convex regression estimator that maintains convergence rates after convexification, with demonstrated finite sample performance through simulations and practical examples.

Contribution

It proposes a novel convexification approach for any existing regression estimator, ensuring convergence properties are preserved in convex regression estimation.

Findings

Convergence rate is maintained after convexification.

Finite sample properties are favorable based on simulations.

Method is demonstrated in practical applications.

Abstract

A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the convex envelope of a sample of the approximation obtained. We prove that the uniform rate of convergence of the estimator is maintained after the convexification is applied. The finite sample properties of the new estimator are investigated by means of a simulation study and the application of the new method is demonstrated in examples.