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Nonparametric regression as an example of model choice

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  • Davies, Paul Lyndon
  • Gather, Ursula
  • Weinert, Henrike

Abstract

Nonparametric regression can be considered as a problem of model choice. In this paper we present the results of a simulation study in which several nonparametric regression techniques including wavelets and kernel methods are compared with respect to their behaviour on different test beds. We also include the taut-string method whose aim is not to minimize the distance of an estimator to some ?true? generating function f but to provide a simple adequate approximation to the data. Test beds are situations where a ?true? generating f exists and in this situation it is possible to compare the estimates of f with f itself. The measures of performance we use are the L2 and the L1 norms and the ability to identify peaks.

Suggested Citation

  • Davies, Paul Lyndon & Gather, Ursula & Weinert, Henrike, 2006. "Nonparametric regression as an example of model choice," Technical Reports 2006,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200624
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    1. Davies, P. L., 2003. "Approximating data and statistical procedures. I. Approximating data," Technical Reports 2003,07, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
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    Cited by:

    1. Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.
    2. Davies, P. Laurie & Kovac, Arne & Meise, Monika, 2007. "Confidence sets and non-parametric regression," Technical Reports 2007,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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