Frontier estimation and extreme value theory

TL;DR

This paper integrates extreme value theory into nonparametric frontier estimation, deriving new estimators with asymptotic properties and applying them to real-world data to improve boundary estimation accuracy.

Contribution

It introduces novel asymptotically Gaussian estimators for monotone frontiers using extreme value theory, extending existing asymptotic results for the free disposal hull.

Findings

New asymptotic confidence bands for boundary functions

Monte Carlo experiments demonstrate estimator performance

Application to postal service data shows practical utility

Abstract

In this paper, we investigate the problem of nonparametric monotone frontier estimation from the perspective of extreme value theory. This enables us to revisit the asymptotic theory of the popular free disposal hull estimator in a more general setting, to derive new and asymptotically Gaussian estimators and to provide useful asymptotic confidence bands for the monotone boundary function. The finite-sample behavior of the suggested estimators is explored via Monte Carlo experiments. We also apply our approach to a real data set based on the production activity of the French postal services.