Nonparametric and Semiparametric Estimation of Additive Models with Both Discrete and Continuous Variables under Dependence
Christine Camlong-Viot, Juan M. Rodríguez Póo, Philippe Vieu · Contributions to statistics · 2006
This paper is concerned with the estimation of nonparametric and semiparametric additive models in the presence of discrete variables. The main feature of our work is to deal with possibly dependent variables. Our methodology can be seen as well as an unifying presentation of several different situations, as extensions to dependence structures of several recent advances obtained in the usual i.i.d. case. Among the different estimation procedures, the method introduced by Linton and Nielsen (1995), 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 L 2 distance between the additive nonparametric component and its correspondent linear direction.