Robust estimates in generalized partially linear models

Abstract

In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,μ_i)$ with $μ_i=H(η(t_i)+\mathbf{x}_i^{$\mathrm{T}$}β)$, for some known distribution function F and link function H. It is shown that the estimates of $β$ are root-n consistent and asymptotically normal. Through a Monte Carlo study, the performance of these estimators is compared with that of the classical ones.

Published at http://dx.doi.org/10.1214/009053606000000858 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)