Aprimoramento do teste da razão de verossimilhanças em modelos de regressão beta-prime

Abstract

This paper deals with the issue of testing hypotheses in beta-prime regression models in small and moderate-sized samples. We focus on the likelihood ratio test, which is unreliable when the sample size is not large enough to guarantee a good approximation between the exact distribution of the test statistic and the corresponding chi-squared asymptotic distribution. Bartlett, Skovgaard and Bartlett-bootstrap corrections typically attenuate the size distortion of the test. Here, we derive a Bartlett correction and a Skovgaard adjustment for the likelihood ratio test on beta-prime regression models. We numerically compare the usual, corrected and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level. The analytically corrected tests perform with the advantage of not requiring computationally intensive calculations. We present a real data application to illustrate the usefulness of the modified tests.