On the empirical Bayes approach to adaptive filtering

E. Belitser, B.Y. Levit

    Research output: Contribution to journalArticleAcademicpeer-review

    2 Citations (Scopus)

    Abstract

    We consider an empirical Bayes approach to adaptive estimation in a sequence model corresponding, via Faurier transform, to the pointwise recovery of a signal in the continuous Gaussian white noise model. The vell-knovn minimax approach to this problem is closely related to the Bayes filtering of stationary Gaussian processes corrupted by a Gaussian vhite noise. The proposed method of adaptive filtering combines two well-known techniques: the Wiener filter and empirical Bayes approach. Our main purpose is to demonstrate how this method works, in a prototypical nonparametric problem. We also discuss an interesting phenomenon of (Bayesian) under- and oversmoothing.
    Original languageEnglish
    Pages (from-to)131-154
    JournalMathematical Methods of Statistics
    Volume12
    Issue number2
    DOIs
    Publication statusPublished - 2003

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