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Fronk, Eva-Maria and Fahrmeir, Ludwig (1998): Function estimation with locally adaptive dynamic models. Collaborative Research Center 386, Discussion Paper 135 [PDF, 428kB]

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We present a nonparametric Bayesian method for fitting unsmooth 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 states 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 regression with local bandwidth or smoothing parameter selection. Performance is illustrated with simulated data, including unsmooth examples constructed for wavelet shrinkage, and by an application to CP6 sales data.

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