Empirical Bayesian test of the smoothness

E.N. Belitser, F. Enikeeva

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    Samenvatting

    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.
    Originele taal-2Engels
    Plaats van productieEindhoven
    UitgeverijEurandom
    Aantal pagina's27
    StatusGepubliceerd - 2005

    Publicatie series

    NaamReport Eurandom
    Volume2005014
    ISSN van geprinte versie1389-2355

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