S-Estimation for Penalized Regression Splines
本文提出用S估计替代最小二乘法来拟合惩罚回归样条模型，使模型对异常值更稳健，同时保持捕捉非线性趋势的灵活性，并通过模拟和真实数据验证了有效性。
This article is about S-estimation for penalized regression splines. Penalized regression splines are one of the currently most used methods for smoothing noisy data. The estimation method used for fitting such a penalized regression spline model is mostly based on least squares methods, which are known to be sensitive to outlying observations. In real-world applications, outliers are quite commonly observed. There are several robust estimation methods taking outlying observations into account. We define and study S-estimators for penalized regression spline models. Hereby we replace the least squares estimation method for penalized regression splines by a suitable S-estimation method. By keeping the modeling by means of splines and by keeping the penalty term, though using S-estimators instead of least squares estimators, we arrive at an estimation method that is both robust and flexible enough to capture nonlinear trends in the data. Simulated data and a real data example are used to illustrate the effectiveness of the procedure. Software code (for use with R) is available online.