Sammendrag
Penalized regression splines are one of the popular methods for smoothing noisy data. The estimation methods used for fitting such a penalized regression spline model are usually based on least squares methods, which are known to be sensitive to outlying observations. The main objective of this work is to extend the estimation method for penalized regression splines to that of S-estimation. We used the Tukey’s biweight family of loss functions to estimate the S-estimates. We propose a computationally fast procedure for estimating penaliz ed regression spline models via S-estimators. Simulated data and real data examples are used to illustrate the effectiveness of the procedure. The results of these examples indicate that S-estimates for penalized regression splines are more appropriate for data with outliers. Additionally, We study estimation and model selection on both the fixed and random effects in the setting of linear mixed models that are estimated using outlier robust S-estimators. The derived marginal and conditional information criteria are in the style of Akaike’s information criterion but avoid the use of a fully specified likelihood by a suitable S-estimation approach that minimizes a scale function. We derive the appropriate penalty terms and provide an implementation using R. The setting of semiparametric additive models fit with penalized regression splines, attractive because of its link with mixed models, is worked out as a specific application. Simulated data and real data examples illustrate the effectiveness of the proposed criteria.