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Robust estimators in a generalized partly linear regression model under monotony constraints. (English) Zbl 1439.62122
Summary: 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. Under regularity conditions, we derive consistency results for the nonparametric function estimators as well as consistency and asymptotic distribution results for the regression parameter estimators. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. 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. The proposal is illustrated on a real data set.

##### MSC:
 62G35 Nonparametric robustness 62G30 Order statistics; empirical distribution functions 62J05 Linear regression; mixed models 65D07 Numerical computation using splines 62P10 Applications of statistics to biology and medical sciences; meta analysis 62P20 Applications of statistics to economics
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