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dc.contributor.authorAbramovich, F.en
dc.contributor.authorSapatinas, Theofanisen
dc.contributor.authorSilverman, B. W.en
dc.creatorAbramovich, F.en
dc.creatorSapatinas, Theofanisen
dc.creatorSilverman, B. W.en
dc.description.abstractWe discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion that is common to most applications. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relationship between the hyperparameters of the prior model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relationship gives insight into the meaning of the Besov space parameters. Moreover, the relationship established makes it possible in principle to incorporate prior knowledge about the function's regularity properties into the prior model for its wavelet coefficients. However, prior knowledge about a function's regularity properties might be difficult to eliciten
dc.description.abstractwith this in mind, we propose a standard choice of prior hyperparameters that works well in our examples. Several simulated examples are used to illustrate our method, and comparisons are made with other thresholding methods. We also present an application to a data set that was collected in an anaesthesiological study. © 1998 Royal Statistical Society.en
dc.sourceJournal of the Royal Statistical Society.Series B: Statistical Methodologyen
dc.subjectNonparametric regressionen
dc.subjectWavelet transformen
dc.subjectAdaptive estimationen
dc.subjectBesov spacesen
dc.subjectBayes modelen
dc.titleWavelet thresholding via a Bayesian approachen
dc.description.endingpage749Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied SciencesΤμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics
dc.description.notes<p>Cited By :322</p>en
dc.source.abbreviationJ.R.Stat.Soc.Ser.B Stat.Methodol.en
dc.contributor.orcidSapatinas, Theofanis [0000-0002-6126-4654]

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