When the data used to fit a nonparametric regression model are contaminated with outliers we need to use a robust estimator of scale in order to introduce robust estimation of the regression function. we develop a family of M-estimators for scale parameter constructed from consecutive differences of regression responses. We quantify the robustness of each estimator via the maxbias. We use this measure as a basis for deriving the asymptotic breakdown point of the estimator.
