Empirical Bayesian test of the smoothness

E.N. Belitser, F. Enikeeva

    Research output: Book/ReportReportAcademic

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    Abstract

    In the context of adaptive nonparametric curve estimation problem, a common assumption is that a function (signal) to estimate belongs to a nested family of functional classes, parameterized by a quantity which often has a meaning of smoothness amount. It has already been realized by many that the problem of estimating the smoothness is not sensible. What then can be inferred about the smoothness? The paper attempts to answer this question. We consider the implications of our results to hypothesis testing. We also relate them to the problem of adaptive estimation. The test statistic is based on the marginalized maximum likelihood estimator of the smoothness for an appropriate prior distribution on the unknown signal.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherEurandom
    Number of pages27
    Publication statusPublished - 2005

    Publication series

    NameReport Eurandom
    Volume2005014
    ISSN (Print)1389-2355

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