Frontier estimation via kernel regression on high power-transformed data

TL;DR

This paper introduces a novel kernel regression method on high power-transformed data for estimating the frontier of multidimensional samples, with proven convergence properties and demonstrated finite sample performance.

Contribution

It proposes a new frontier estimation technique using kernel regression on power-transformed data, with theoretical convergence guarantees and practical effectiveness.

Findings

Estimator achieves complete convergence and asymptotic normality.

Good performance demonstrated on finite sample scenarios.

Conditions on parameters ensure theoretical properties.

Abstract

We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the bandwidth of the kernel goes to zero. We give conditions on these two parameters to obtain complete convergence and asymptotic normality. The good performance of the estimator is illustrated on some finite sample situations.