Improved Likelihood Ratio Tests in Power Series Generalized Nonlinear Models

摘要

The power series generalized nonlinear models, recently proposed in the literature, is a class of discrete nonlinear regression models with the aim of generalizing several widely known counting regression models such as the generalized Poisson and generalized negative binomial, among others. In this paper, improved versions for likeli-hood ratio statistic for hypothesis testing in this class are presented. Performance of bootstrap-based improved versions of the test statistics are addressed. Based on Bartlett correction theory, it is possible to ensure, for the improved statistics, an asymptotic χ~2 distribution up to order O(n~(-1)). We proposed a bootstrap-based numeric estimation of such correction factor. Monte Carlo simulations show that the proposed improvements display reliable finite-sample behaviour, outperforming the original tests. The usefulness of the improved tests is also shown by means of a real data set.