Estudo sobre má especificação na família de posição e escala

Abstract

The likelihood-based theory is often used in solving problems in various areas of statistics. One of the basic assumptions of inference based on this theory is that the chosen model correctly summarizes the data. When this does not happen, the usual procedures can result in misleading conclusions. In this sense, although the problem of misspecification can appear in several contexts, there are few papers dealing with this topic. Therefore, this work is designed to study the main inferential procedures in the context of misspecification and, in particular, hypotheses testing. Robust versions of the usual statistics are presented when the model is misspecified, considering location-scale family models. In addition, the performance of these statistics is studied in the presence of misspecification in regression models, considering simple and composite hypotheses and, finally, a simulation study is performed. It is noted that the robust versions of the statistics present good results, both in the context of independent and identically distributed samples as well as in the context of regression models.