Robust estimates in generalized partially linear models

TL;DR

This paper develops a family of robust estimation methods for both parametric and nonparametric parts of generalized partially linear models, improving resilience to data anomalies.

Contribution

It introduces robust estimators for generalized partially linear models that are root-n consistent and asymptotically normal, with demonstrated superior performance over classical methods.

Findings

Estimators are root-n consistent and asymptotically normal.

Monte Carlo simulations show improved robustness.

Performance surpasses classical estimators in simulations.

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 $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,\mu_i)$ with $\mu_i=H(\eta(t_i)+\mathbf{x}_i^{$\mathrm{T}$}\beta)$, for some known distribution function F and link function H. It is shown that the estimates of $\beta$ 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.