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Data-Adaptive Kernel Estimation

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Nonparametric Functional Estimation and Related Topics

Part of the book series: NATO ASI Series ((ASIC,volume 335))

Abstract

Kernel estimators are by now well established for curve estimation in a broad variety of problems. Here the regression problem is studied. Basic properties are summarized and a comparison with other popular estimators is then made. The choice of bandwidth or smoothing parameter is decisive in many ways; a data-adaptive optimization of this choice offers many advantages. An iterative plug-in rule based on the asymptotic formula is introduced and contrasted with cross-validation type selectors. The latter prove to be inferior asymptotically and in simulations mainly due to their large variability. A difficult problem is then choosing the bandwidth appropriately when residuals are correlated. Introducing a second tuning parameter to adapt to the unknown correlation structure leads to a solution which shows good properties in theory and practice. It is important that this may be achieved without postulating some parametric model for the residual time series.

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Author information

Authors and Affiliations

  1. Zentralinstitut für seelische Gesundheit I5, 6800, Mannheim 1, Germany

    Theo Gasser

  2. Sonderforschungsbereich 123, Universität Heidelberg, Im Neuenheimer Feld 294, 6900, Heidelberg, Germany

    Eva Herrmann

Authors
  1. Theo Gasser
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  2. Eva Herrmann
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Editor information

Editors and Affiliations

  1. Intercollege Division of Statistics, University of California, Davis, California, USA

    George Roussas

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© 1991 Springer Science+Business Media Dordrecht

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Gasser, T., Herrmann, E. (1991). Data-Adaptive Kernel Estimation. In: Roussas, G. (eds) Nonparametric Functional Estimation and Related Topics. NATO ASI Series, vol 335. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3222-0_5

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  • DOI: https://doi.org/10.1007/978-94-011-3222-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5420-1

  • Online ISBN: 978-94-011-3222-0

  • eBook Packages: Springer Book Archive

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