Resistant Selection of the Smoothing Parameter for Smoothing Splines

Statistics and Computing (Impact Factor: 1.62). 01/1998; 11(98.06). DOI: 10.1023/A:1008975231866
Source: RePEc


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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    • "A detailed exposition on these alternatives can be found in Härdle (1990) and Härdle et al. (2004). However, these procedures may not be robust and their sensitivity to anomalous data was discussed by several authors, including Leung et al. (1993), Wang and Scott (1994), Boente et al. (1997), Cantoni and Ronchetti (2001) and Leung (2005). Wang and Scott (1994) note that, when estimating the regression function, in the presence of outliers, the least squares cross–validation function is nearly constant on its whole domain and thus, essentially worthless for the purpose of choosing a bandwidth. "
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    ABSTRACT: We introduce and compare several robust procedures for bandwidth selection when estimating the variance function. These bandwidth selectors are to be used in combination with the robust scale estimates introduced by Boente et al. (2010a). We consider two different robust cross-validation strategies combined with two ways for measuring the cross-validation prediction error. The different proposals are compared with non robust alternatives using Monte Carlo simulation. We also derive some asymptotic results to investigate the large sample performance of the corresponding robust data-driven scale estimators.
    Computational Statistics & Data Analysis 06/2012; 56(6). DOI:10.1016/j.csda.2011.10.002 · 1.40 Impact Factor
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    • "On the other hand, if we define the estimator by solving an implicit equation, one can follow the approach introduced by [9] where a robustified quasi-likelihood estimator is developed. "
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    ABSTRACT: In this paper, we focus on nonparametric regression estimation for the parameters of a discrete or continuous distribution, such as the Poisson or Gamma distributions, when anomalous data are present. The proposals are nonparametric versions of robust estimators that have been introduced in the parametric setting for generalized linear models. We present two families of estimators and their asymptotic behaviour is studied. Through a Monte Carlo study we compare the performance of the proposed estimators with the classical ones. We also introduce a resistant cross–validation method to choose the smoothing parameter.
    Statistics [?] Probability Letters 12/2011; 81(12). DOI:10.1016/j.spl.2011.08.007 · 0.60 Impact Factor
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    • "Furthermore, note that outliers can also affect data-based methods used to determine the tuning (or penalty) constants involved in the smoothing steps of the GLSA algorithm (see, for example, Cantoni and Ronchetti, 2001a). Intuitively, one does not want to penalize fits that do not predict well those observations that are potential outliers. "
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    ABSTRACT: We are interested in a class of unsupervised methods to detect possible disease outbreaks, i.e. rapid increases in the number of cases of a particular disease that deviate from the pattern observed in the past. When analyzing data generated by surveillance systems following a large number of diseases and / or health districts, it is often of interest to have a methodology to flag potential outbreaks without requiring the intervention of a data analyst. The motivating application for this paper deals with detecting outbreaks using Generalized Additive Models to model weekly counts of certain infectious diseases. Case counts of relatively prevalent diseases or viral infections (e.g. influenza, HIV, Hepatitis C) typically exhibit strong non- linear temporal patterns. Generalized Additive Models are a natural tool to model these data.
    Journal of the American Statistical Association 06/2011; 106(494):719-731. DOI:10.1198/jasa.2011.tm09654 · 1.98 Impact Factor
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