Distribuição da estatística de Wald em amostras finitas para modelos GAMLSS paramétricos

Abstract

In parametric regression models, we often want to test hypotheses regarding the values of their parameters. Specifically, when we depart from the general linear model (random errors with a Normal distribution), the Wald test is one of the most commonly used for this purpose. The square root of the statistic used in this test, known as the Wald statistic, has a standard asymptotic Normal distribution under the null hypothesis. However, various statistical software approximates the distribution of the square root of the Wald statistic with the t-distribution. The main objective of this study is to investigate whether, for regression models considering different distributions of the response variable, the distribution of the square root of the Wald statistic is better approximated in small to moderate samples by the t-distribution or the standard Normal distribution. Conclusions will be drawn from conducting Monte Carlo simulation studies and will be considered for response variables belonging to both exponential and non-exponential families.