PN-III-P4-ID-PCE-2020-1112
Robust Empirical Likelihood and Related Methods for Semiparametric Models
Abstract
Empirical likelihood (EL) is a powerful and currently widely used approach for developing efficient nonparametric statistical methods. The EL was introduced by Owen (1988) and since then many papers have appeared on this topic making various contributions to different inferential problems. The purpose of this project is to introduce robust versions of EL and other alternative new statistical methods for semiparametric moment condition models, as well as for semiparametric two sample density ratio models. The main approach will be based on using dual representations of divergences between probability measures, projections of probability measures in the sense of divergences and truncation techniques, allowing obtaining large classes of estimators and test statistics for the aforementioned semiparametric models. Extensions of SmoothMD estimators and model check procedures for the framework of general conditional moment condition models will also be studied. New tests for conditional independence based on kernel smoothing and applications to graphical models inference will also be developed. Theoretical properties of the new statistical methods will be studied, with a special emphasis on robustness properties. Advantages with respect to other existing methods will also be analyzed. In order to assess the finite sample performances of the proposed methods, we will provide extended Monte Carlo simulation studies, comparisons, as well as applications.