Correções da estatística da razão de verossimilhanças em modelos de regressão beta prime

Abstract

This dissertation deals with Skovgaard’s correction for the likelihood ratio statistic applied to the reparametrized beta prime regression model in terms of μ and ϕ by BOURGUIGNON et al. (2018). The likelihood ratio test is one of the most commonly used methods for testing hypotheses about parameters in a regression model due to its simplicity. The Beta Prime regression model is convenient for modeling asymmetric data and serves as an alternative to Generalized Linear Models (GLM) when dealing with skewed data. However, the test can be significantly distorted when the sample size is not large enough. Additionally, it is essential to note that the chi-squared distribution, χ2, may not be a good approximation for the exact null distribution of the likelihood ratio statistic in samples of small or moderate sizes. To improve this approximation, the usual strategy is to replace the likelihood ratio statistic with its corrected versions. Monte Carlo simulations were conducted to evaluate the performance of the corrected statistic. Finally, two applications to real data are presented.