
Архив публикацийТезисыXXIая конференцияRobust Fitting Penalized Regression Spline ModelsRussia, 127994, Moscow, Vadkovsky per., 3A 1 стр. (принято к публикации)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 Sestimators for penalized regression spline models. Hereby we replace the least squares estimation method for penalized regression splines by a suitable Sestimation method. By keeping the modeling by means of splines and by keeping the penalty term, though using Sestimators 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. The main purpose of this paper is to propose robust penalized regression splines that are able to resist the potentially damaging effect of outliers in the sample, and that do not require the separate estimation of the residual scale. To achieve these goals we propose to compute penalized Sregression estimators. In the unpenalized case, these estimators are consistent, asymptotically normal, and have highbreakdown point regardless of the dimension of the vector of regression coeficients. First we show that the solution to the penalized Sregression problem can be written as the solution of a weighted penalized least squares problem. This representation naturally leads to an iterative algorithm to compute these estimators. We also study how to robustly select the penalty parameter when there may be outliers in the data. We propose a robust penalty parameter selection criteria based on generalized crossvalidation that also borrows from the weighted penalized least squares representation of the penalized Sregression estimator. Extensive simulation studies show that our algorithm works well in practice and that the resulting regression function estimator is robust to the presence of outliers in the data. 