General inference in semiparametric models through divergences and the duality technique with applications

In this paper, we extend the dual divergence approach to general semiparametric models and study dual divergence estimators for semiparametric models. Asymptotic properties such as consistency, asymptotic normality of the proposed estimators are deeply investigated by mean the sophisticated modern empirical theory. We investigate the exchangeably weighted estimators in this setting and establish the consistency. We finally consider the functional $M$-estimator and obtain its weak convergence result.