Semi-parametric transformation boundary regression models

TL;DR

This paper introduces semi-parametric boundary regression models with transformation techniques to improve error-covariate independence, providing consistent estimators and demonstrating their effectiveness through simulations.

Contribution

It develops a new approach for estimating transformation parameters and boundary curves in nonparametric regression with one-sided errors, ensuring uniform consistency.

Findings

Estimator for transformation parameter is uniformly consistent.

Boundary curve estimation is consistent under mild conditions.

Simulation study confirms good finite-sample performance.

Abstract

In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on stritcly increasing and continuous transformations. In view of estimating the tranformation parameter, we use a minimum distance approach and show the uniform consistency of the estimator under mild conditions. The boundary curve, i.e. the regression function, is estimated applying a smoothed version of a local constant approximation for which we also prove the uniform consistency. We deal with both cases of random covariates and deterministic (fixed) design points. To highlight the applicability of the procedures and to demonstrate their performance, the small sample behavior is investigated in a simulation study using the so-called Yeo-Johnson transformations.