Avaliação de testes de hipóteses assintóticos no modelo de regressão Lindley-unitária: um estudo de simulação e aplicação

Abstract

Inference in regression models can be compromised in small or moderate samples, since classical tests such as the likelihood ratio, Wald, score, and gradient tests tend to exhibit size distortions, leading to incorrect statistical decisions. This study aims to evaluate and compare the performance of these four tests, as well as a corrected version of the Wald test with second-order refinements, within the Unit-Lindley regression model, which is suitable for continuous variables restricted to the interval (0,1). For this purpose, a Monte Carlo simulation study was conducted, varying the sample size, the number of model parameters, and the length of the parameter vector under test. The results indicate that the performance of the asymptotic tests deteriorates as model complexity increases, especially in small samples. In general, the traditional Wald test was systematically liberal, increasing the risk of type I errors, whereas the score test showed markedly conservative behavior, implying a loss of statistical power. The corrected version of the Wald test presented significant improvements, but the gradient test stood out for its superior robustness and consistency. It maintained rejection rates very close to nominal levels, even in the most demanding scenarios, and benefits from greater computational simplicity, as it does not require the computation of the information matrix. It is concluded that the gradient test represents the most advisable alternative for practical analyses in this context, offering a combination of accuracy and efficiency.