Resistant Selection of the Smoothing Parameter for Smoothing Splines
ABSTRACT Robust automatic selection techniques of the smoothing parameter of a smoothing spline are introduced. They are based on a robust predictive error criterion and can be viewed as robust version of Cp and cross-validation. They lead to smoothing splines which are stable and reliable in terms of mean squared error over a large spectrum of model's distributions.
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ABSTRACT: In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit approach to the functional data setting. Our approach combines robust projection-pursuit with different smoothing methods. Consistency of the estimators are shown under mild assumptions. The performance of the classical and robust procedures are compared in a simulation study under different contamination schemes.The Annals of Statistics 03/2012; 39(6). · 2.53 Impact Factor
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ABSTRACT: Generalized linear models are a widely used method to obtain parametric estimates for the mean function. They have been further extended to allow the relationship between the mean function and the covariates to be more flexible via generalized additive models. However, the fixed variance structure can in many cases be too restrictive. The extended quasilikelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covariates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this article, we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.Biometrics 06/2011; 68(1):31-44. · 1.41 Impact Factor
- European Journal of Cancer - EUR J CANCER. 01/2011; 47.