Testing for linearity in boundary regression models with application to maximal life expectancies

TL;DR

This paper develops goodness-of-fit tests for boundary regression models where errors are almost surely negative, focusing on whether the regression function is affine, with applications to analyzing maximal life expectancies.

Contribution

It introduces new tests for linearity in boundary regression models with negative errors and studies their asymptotic and finite-sample properties, applied to life expectancy data.

Findings

Tests effectively identify affine regression functions.

Asymptotic distributions enable size approximation.

Finite-sample simulations validate test performance.

Abstract

We consider a regression model with errors that are a.s. negative. Thus the regression function is not the expected value of the observations but the right endpoint of their support. We develop two goodness-of-fit tests for the hypotheses that the regression function is an affine function, study the asymptotic distributions of the test statistics in order to approximately fix the sizes of the tests, derive their finite-sample properties based on simulations and apply them to life expectancy data.