Robust estimation in Generalized Partially Linear Single-Index Models.

BOENTE, GRACIELA; RODRIGUEZ, DANIELA

Valladolid

Congreso; ICORS 2011, (International Conference on Robust Statistics).; 2011

Universidad de Valladolid

Julio de 2011. Valladolid, Espa~na. par {Presentaci´on del trabajo} extit{lqlq q q}. G. Boente y D. Rodriguez. (Expositor: D. Rodriguez). A natural generalization of the well known generalized linear models is to allow only some of the predictors to be modeled linearly while others are modeled nonparametrically. However, this model can face the so called lqlq curse of dimensionality q q problem that can be solved by imposing a nonparametric dependence on some unknown projection of the carriers. More precisely, we assume that the observations $left(y_i, {x_i,t_i} ight)$, $1le ile n$, are such that $t_iin eal^q$, $x_iin eal^p$ and $y_i|left({x_i,t_i} ight)sim Fleft(cdot, mu_i ight)$ with $mu_i=H left (eta(alfa raspt_i)+x_i raspbe ight)$, for some known distribution function $F$ and link function $H$. The function $eta: eal o eal$ and the parameters $alfa$, $be$ are unknown and to be estimated. This model, denoted extsc{gplsim}, is known as the extsl{generalized partly linear single-index} model. In this talk, we introduce a family of robust estimates for the parametric and nonparametric components under model extsc{gplsim}. It is shown that the estimates of $alfa$ and $be$ are root--$n$ consistent and asymptotically normally distributed. Through a Monte Carlo study, we compare the performance of the proposed estimators with that of the classical ones.