Frontier estimation with local polynomials and high power-transformed data

TL;DR

This paper introduces a novel frontier estimation method using local polynomial regression on high power-transformed data, achieving almost complete convergence under specific conditions, with demonstrated good finite sample performance.

Contribution

It proposes a new estimator based on local polynomial regression on power-transformed data, with theoretical convergence guarantees and practical performance evaluation.

Findings

Estimator achieves almost complete convergence.

Asymptotic bias and variance are characterized.

Performs well in finite sample scenarios.

Abstract

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