On hypothesis testing inference in location-scale models under model misspecification

Abstract

The likelihood ratio, Wald, score and gradient test statistics can result in misleading conclusions when the assumed parametric model to the data at hand is not correctly specified. To overcome this issue, robust versions of these test statistics have been proposed in the statistic literature under model misspecification. In this paper, we address the issue of performing hypothesis testing inference in location-scale models under model misspecification. Monte Carlo simulation experiments are carried out to verify the performance of the robust test statistics, as well as usual test statistics (i.e. non-robust), in the class of location-scale models under model misspecification. The simulation results reveal that the robust tests we propose are more reliable than the usual tests since they lead to an accurate inference. An empirical application to real data is considered for illustrative purposes.