On interval and point estimators based on a penalization of the modified profile likelihood

In the presence of a nuisance parameter, one widely shared approach to likelihood inference on a scalar parameter of interest is based on the profile likelihood and its various modifications. In this paper, we add a penalization to the modified profile likelihood, which is based on a suitable matching prior, and we discuss the frequency properties of interval estimators and point estimators based on this penalized modified profile likelihood. Two simulation studies are illustrated, and we indicate the improvement of the proposed penalized modified profile likelihood over its counterparts.