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Title: Penalized splines with censored data Authors:  Jesus Orbe - University of the Basque Country (Spain) [presenting]
Jorge Virto - University of the Basque Country (Spain)
Abstract: The problem of nonparametric curve fitting is considered in the specific context of censored data. That is, we do not observe completely the sample, because some of the data values are censored. This situation is very usual in survival or duration analysis. When the available data are complete, that is, without censored data, the problem of nonparametric curve fitting has been extensively studied and there is an enormous literature on this area. There are different methods, as for example, kernel smoothers and spline smoothers. Our proposal is situated under the splines approach. Thus, an extension of the penalized splines approach is provided for the case of censored data samples. This method works together the usual B-spline regression techniques and the smoothing spline approach reducing considerably the dimension of the estimation problem in large samples in comparison with the smoothing splines case. Using various simulation studies we analyze the effectiveness of the proposed method and show that the performance are quite satisfactory. Also a real data set is used to illustrate the proposed methodology and it is shown as a well alternative when we do not know the functional form on censored regression models.