Small-sample likelihood inference in extreme-value regression models

TL;DR

This paper develops an adjusted likelihood ratio test for extreme-value regression models, improving accuracy in small samples and comparing its performance with other classical tests through simulations and applications.

Contribution

It introduces a simple, computationally feasible adjustment to the likelihood ratio test for extreme-value regression models, enhancing small-sample inference accuracy.

Findings

Adjusted likelihood ratio test outperforms classical tests in simulations.

The adjustment term has a simple form suitable for standard software.

Simulations show the gradient test is less accurate than the adjusted likelihood ratio test.

Abstract

We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as \c{hi}2 with a high degree of accuracy. Although the adjusted statistic requires more computational effort than its unadjusted counterpart, it is shown that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. Further, we compare the finite sample performance of the three classical tests (likelihood ratio, Wald, and score), the gradient test that has been recently proposed by Terrell (2002), and the adjusted likelihood ratio test obtained in this paper. Our simulations favor the latter. Applications of our results are presented. Key words: Extreme-value regression; Gradient test; Gumbel distribution; Likelihood ratio test; Nonlinear models; Score test; Small-sample adjustments; Wald test.