Intervalos de confiança baseados em Deviance para os hiperparâmetros em modelos estruturais

Abstract

The objective of this work is to compare different interval procedures for hyperparameters of structural models. The usual procedures include the asymptotic method, based on the asymptotic distribuition of the maximum likelihood estimator, as well as a bootstrap based confidence interval. This work presents three methods based on the likelihood test. The first is a marginal aproximation of confidence regions, the second is based on the profile deviance function and the third method is the Signed root Deviance Profile. Those methods avoid the problems associated with the asymptotic method for small samples, as intervals generated outside the parametric space. They are also an alternative for bootstrap methods, being computationaly more efficient. A comparison is performed, via Monte Carlo simulation, in order to establish advantages and disadvantages for each method. The results show that these methods possess a better coverage rate than the asymptotic and bootstrap procedures.