Uniform strong consistency of a frontier estimator using kernel regression on high order moments

TL;DR

This paper proves the uniform strong consistency and convergence rate of a kernel-based high order moments estimator for the frontier of a random pair, under certain distributional assumptions.

Contribution

It establishes the uniform strong consistency and convergence rate of a frontier estimator using kernel regression on high order moments, extending previous work.

Findings

Estimator is strongly uniformly consistent on compact sets

Convergence rate is derived under Hall class distribution assumptions

Results improve understanding of frontier estimation accuracy

Abstract

We consider the high order moments estimator of the frontier of a random pair introduced by Girard, S., Guillou, A., Stupfler, G. (2012). {\it Frontier estimation with kernel regression on high order moments}. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.