Function estimation with locally adaptive dynamic models

Stefan Lang, Eva-Maria Pronk and Ludwig Fahrmeir
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Stefan Lang: University of Munich
Eva-Maria Pronk: University of Munich
Ludwig Fahrmeir: University of Munich

Computational Statistics, 2002, vol. 17, issue 4, No 3, 479-499

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.

Keywords: adaptive smoothing; MCMC; nonparametric Bayesian regression; random walk priors; unsmooth functions; variable smoothing parameter (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/s001800200121

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