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S-Estimation for Penalized Regression Splines
Journal Contribution - Journal Article
This paper is about S-estimation for penalized regression splines. Penalized re-gression splines are one of the currently most used methods for smoothing noisydata. The estimation method used for ¯tting such a penalized regression splinemodel is mostly based on least squares methods, which are known to be sensitiveto outlying observations. In real world applications, outliers are quite commonlyobserved. There are several robust estimation methods taking outlying observationsinto account. We de¯ne and study S-estimators for penalized regression spline mod-els. Hereby we replace the least squares estimation method for penalized regressionsplines by a suitable S-estimation method. By keeping the modeling by means ofsplines and by keeping the penalty term, though using S-estimators instead of leastsquares estimators, we arrive at an estimation method that is both robust and °exi-ble enough to capture non-linear trends in the data. Simulated data and a real dataexample are used to illustrate the e®ectiveness of the procedure.
Journal: Journal of Computational and Graphical Statistics
Number of pages: 16
Keywords:M-estimator, Penalized least squares method