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Partially linear models are important tools in statistical modeling, combining the flexibility of non–parametric models and the simple interpretation of linear models. Monotonicity constraints appear naturally in certain problems when the response is known to increase with one of the covariates. Estimation methods for partially linear models with monotonicity constraints have been proposed in recent years. These methods have a good performance when all the observations follow the assumed model. However, if a small proportion of atypical observations is present in the sample, these estimators become unreliable. A robust estimation method for these models is proposed and applied to two real data sets. A Monte Carlo simulation study is performed, in which the proposed estimators are compared to existing ones in different situations, both with clean and contaminated samples.

Robust estimation in partially linear regression models with monotonicity constraints