Robust estimators in a generalized partly linear regression model under monotony constraints

TL;DR

This paper develops robust estimation methods for a generalized partly linear regression model with a monotonic nonparametric component, using spline-based approaches and score functions to improve robustness, demonstrated through simulations.

Contribution

It introduces a new class of robust estimators for monotone nonparametric components in generalized partly linear models, combining spline methods with bounded score functions.

Findings

Robust estimators perform well in simulations with increasing nonparametric components.

The spline-based approach effectively estimates the monotone function.

The methods are applicable to log-Gamma regression models.

Abstract

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log--Gamma regression model. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log-Gamma regression model with increasing nonparametric component.