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On robust cross-validation for nonparametric smoothing

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  • Oliver Morell
  • Dennis Otto
  • Roland Fried

Abstract

An essential problem in nonparametric smoothing of noisy data is a proper choice of the bandwidth or window width, which depends on a smoothing parameter $$k$$ . One way to choose $$k$$ based on the data is leave-one-out-cross-validation. The selection of the cross-validation criterion is similarly important as the choice of the smoother. Especially, when outliers are present, robust cross-validation criteria are needed. So far little is known about the behaviour of robust cross-validated smoothers in the presence of discontinuities in the regression function. We combine different smoothing procedures based on local constant fits with each of several cross-validation criteria. These combinations are compared in a simulation study under a broad variety of data situations with outliers and abrupt jumps. There is not a single overall best cross-validation criterion, but we find Boente-cross-validation to perform well in case of large percentages of outliers and the Tukey-criterion in case of data situations with jumps, even if the data are contaminated with outliers. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Oliver Morell & Dennis Otto & Roland Fried, 2013. "On robust cross-validation for nonparametric smoothing," Computational Statistics, Springer, vol. 28(4), pages 1617-1637, August.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:4:p:1617-1637
    DOI: 10.1007/s00180-012-0369-2
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    References listed on IDEAS

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    1. Ursula Gather & Karen Schettlinger & Roland Fried, 2006. "Online signal extraction by robust linear regression," Computational Statistics, Springer, vol. 21(1), pages 33-51, March.
    2. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    3. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
    4. Paul Fearnhead & Peter Clifford, 2003. "On‐line inference for hidden Markov models via particle filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 887-899, November.
    5. Lee, Jong Soo & Cox, Dennis D., 2010. "Robust smoothing: Smoothing parameter selection and applications to fluorescence spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3131-3143, December.
    6. Fried, Roland & Bernholt, Thorsten & Gather, Ursula, 2006. "Repeated median and hybrid filters," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2313-2338, May.
    7. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
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    Cited by:

    1. Claudia Köllmann & Björn Bornkamp & Katja Ickstadt, 2014. "Unimodal regression using Bernstein–Schoenberg splines and penalties," Biometrics, The International Biometric Society, vol. 70(4), pages 783-793, December.

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