Nonparametric and Semiparametric Estimation of Additive Models with both Discrete and Continuous Variables under Dependence

This paper is concerned with the estimation and inference of nonparametric and semiparametric additive models in the presence of discrete variables and dependent observations. Among the different estimation procedures, the method introduced by Linton and Nielsen, based in marginal integration, has became quite popular because both its computational simplicity and the fact that it allows an asymptotic distribution theory. Here, an asymptotic treatment of the marginal integration estimator under different mixtures of continuous-discrete variables is offered, and furthermore, in the semiparametric partially additive setting, an estimator for the parametric part that is consistent and asymptotically efficient is proposed. The estimator is based in minimizing the L2 distance between the additive nonparametric component and its correspondent linear direction. Finally, we present an application to show the feasibility of all methods introduced in the paper.