INVESTIGADORES
BOENTE BOENTE Graciela Lina
artículos
Título:
Robust Estimates in Generalized Partially Linear Single-Index Models
Autor/es:
BOENTE, GRACIELA; RODRIGUEZ, DANIELA
Revista:
TEST
Editorial:
SPRINGER
Referencias:
Lugar: Heilderberg; Año: 2012 vol. 21 p. 386 - 411
ISSN:
1133-0686
Resumen:
A natural generalization of the well known generalized linear models is to allow only some of the predictors to be modelled linearly while others are modelled nonparametrically. However, this model can face the so called "curse of dimensionality" problem that can be solved by imposing a nonparametric dependence on some unknown projection of the carriers. More precisely, we assume that the observations $(y_i,x_i,t_i)$, are such that $t_i in R^q$, $x_i in R^p$ and $y_i| ({x_i,t_i})~ F(., mu_i)$ with $mu_i=H(eta(alfa^T t_i)+x_i^Teta)$, for some known distribution function $F$ and link function $H$. The function $eta:R\to R$ and the parameters $alfa$ and $beta$ are unknown and to be estimated. This model is known as the "generalized partly linear single-index" model. In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear single-index model. It is shown that the estimates of $alfa$ and $beta$ 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.