Aperfeiçoamento do teste da razão de verossimilhanças baseado na função de verossimilhança perfilada

Abstract

In Statistics, hypothesis tests are used to make inferences of the parameters of a given probabilistic model. However, it is often convenient to perform inferential study only for a subset of parameters, which are called parameters of interest, and the others, nuisance parameters. Inferences of parameters of interest can be made based on pro led likelihood function. However, making inferences based on this function can lead to inaccurate results when the number of nuisance parameters is large comparing to the sample size. Also, the pro led likelihood function is not genuine. Thus, some basic properties of the likelihood function may not be valid. To mitigate these problems, Barndor -Nielsen (1983) and Severini (1998) proposed adjusted versions of the pro led likelihood function. It is known from the literature that the likelihood ratio statistic, under the null hypothesis, has an asymptotic chi-square distribution. Therefore, for small or moderate samples, the asymptotic distribution is not a good approximation for the exact null distribution. To improve inferences, Sousa (2020) proposed a method for improving the likelihood ratio test, which consists of correcting the tail of the asymptotic null distribution through the chi-square inf. The main aim of this work is to compare the performance of tests based on the likelihood ratio statistic (considering the pro le likelihood function and the modi ed versions) with the improvement method proposed by Sousa (2020) in nite samples. Tests corrected by the bootstrap resampling technique will also be included in the comparison. Speci cally, this comparison will be made by applying the di erent approaches to the Weighted Lindley and Exponentialized Weibull distributions. For that, Monte Carlo simulations will be performed, considering different scenarios. Finally, we performed four numerical examples based on real data sets.