Modified score statistic based on bias reduction

Likelihood inference provides a valuable and general inferential framework for several statistical models, especially parametric ones. However, in some settings maximum likelihood estimators may be affected by a non-negligible presence of bias, thereby requiring research effort towards the mitigation of such issue. As a matter of fact, a branch of statistical literature is specifically devoted to the topic of bias reduction, which constitutes the theoretical background of this thesis. The main purpose of this work is to investigate the performance of a modified score test statistic, defined within the framework of bias reduction in parametric models. The idea beneath this research is to study whether such statistic provides a valuable alternative to the currently-used tests, typically Wald-type ones. In such case, the modified score statistic could be used not only in place of standard likelihood-based tests, but also of Wald-type statistics based on bias reduction. The thesis is organized as follows: in the first chapter, we provide a brief overview on the statistical literature on likelihood inference and bias reduction. In the second chapter, we focus our attention on the modified score test statistic, discussing some computational details and showing numerical examples of the corresponding implementation. In the third chapter, we assess the performance of the modified score statistic by means of simulation studies, considering different possible settings.