Final Report Summary - MAZEST (M- and Z-estimation in semiparametric statistics : applications in various fields)
This ERC project is situated in the area of semiparametric statistics, and more precisely in the development of properties of two particular types of estimators, called semiparametric Z- and M-estimators. Semiparametric models offer a valid alternative to purely parametric ones, which are known to be sensitive to incorrect model specification, and completely nonparametric models, which often suffer from lack of precision and power. A drawback of semiparametric models is, however, that the development of mathematical properties under these models is often a lot harder than under the other two types of models. The main achievement of this project is that it has improved the understanding of how to obtain asymptotic properties of semiparametric Z- and M-estimators. The results of this ERC project have shown the statistical community that it is possible to do correct inference in this type of models, without having to make use of heuristic approximations or ad hoc developments. This is important, since semiparametric models offer important advantages over purely parametric or purely nonparametric models, but inference in this type of models can be an obstacle for its use in practice. The results of this ERC project show how to overcome this obstacle.