Robust inference in generalized partially linear models

BOENTE, GRACIELA; RODRIGUEZ, DANIELA

COMPUTATIONAL STATISTICS AND DATA ANALYSIS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2010 vol. 54 p. 2942 - 2966

0167-9473

In many situations, data follow a generalized partly linear model in which the mean of the responses is modeled, through a link function, linearly on some covariates and nonparametrically on the remaning ones. A new class of robust estimates for the smooth function $eta$, associated to the nonparametric component, and for the parameter $eta$, related to the linear one, is defined. The robust estimators are based on a three step procedure, where large values of the deviance or Pearson residuals are bounded through a score function. These estimators allow to make easier inferences on the regression parameter $eta$ and also improve computationally those based on a robust profile–likelihood approach. The resulting estimates of turn out to be root–n consistent and asymptotically normally distributed. Besides, the empirical influence function allows to study the sensitivity of the estimators to anomalous observations. A robust Wald test for the regression parameter is also provided. Through a Monte Carlo study, the performance of the robust estimators and the robust Wald test is compared with that of the classical ones.