A new Robust algorithm for penalized regression splines based on mode-estimation

The main purpose of present article is proposed an effective method for robust fitting penalized regression splines models. According to such a context a comparative analysis with two common robust techniques, M-type estimator, S-type estimator, and non-robust least squares (LS) for penalized regression splines (PRS) has been implemented. Because the penalized regression splines are recently a common approach to smoothing noisy data for its simplicity, efficiency, and significantly reducing disturbance of outliers and its flexibility in monitoring nonlinear data trends. In many cases, it is difficult to determine the most suitable form and a way of designing a data is needed when faced with many smoothing problems. The executing aspects of fitting precision and robustness of the four estimators have a thorough evaluation of their performance on R codes. A comparative analysis demonstrates that the proposed method can resist the noise effect in both simulated and real data examples compared to other robust estimators with different combinations of contamination. These findings are used as guidance for finding a specific method to pulsing smoothing noisy data