Robust estimation in partially linear regression models

Abstract

A new class of robust estimators via the exponential squared loss function with a tuning parameter are presented for the partially linear regression models. Under some conditions, we show that our proposed estimators for the regression parameter can achieve the highest asymptotic breakdown point of . In addition, we propose the data-driven procedure to choose the tuning parameter. Simulation studies are conducted to compare the performances of the proposed method with the existing methods in terms of the bias, standard deviation (Sd) as well as the mean-squared errors (MSE). The results show that our proposed method has smaller Sd and MSE than the existing methods when there are outliers in the dataset. Finally, we apply the proposed method to analyze the Ragweed Pollen Level data and the salinity data, and the results reveal that our method performs better than the existing methods.