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Function estimation with locally adaptive dynamic models

Author

Listed:
  • Stefan Lang

    (University of Munich)

  • Eva-Maria Pronk

    (University of Munich)

  • Ludwig Fahrmeir

    (University of Munich)

Abstract

Summary We present a nonparametric Bayesian method for fitting unsmooth and highly oscillating functions, which is based on a locally adaptive hierarchical extension of standard dynamic or state space models. The main idea is to introduce locally varying variances in the state equations and to add a further smoothness prior for this variance function. Estimation is fully Bayesian and carried out by recent MCMC techniques. The whole approach can be understood as an alternative to other nonparametric function estimators, such as local or penalized regression with variable bandwidth or smoothing parameter selection. Performance is illustrated with simulated data, including unsmooth examples constructed for wavelet shrinkage, and by an application to sales data. Although the approach is developed for classical Gaussian nonparametric regression, it can be extended to more complex regression problems.

Suggested Citation

  • Stefan Lang & Eva-Maria Pronk & Ludwig Fahrmeir, 2002. "Function estimation with locally adaptive dynamic models," Computational Statistics, Springer, vol. 17(4), pages 479-499, December.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200121
    DOI: 10.1007/s001800200121
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    References listed on IDEAS

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    Cited by:

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    3. Heim, S. & Fahrmeir, L. & Eilers, P.H.C. & Marx, B.D., 2007. "3D space-varying coefficient models with application to diffusion tensor imaging," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6212-6228, August.
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