Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/96486
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dc.contributor.authorLian, Hengen
dc.date.accessioned2013-12-05T02:57:03Zen
dc.date.accessioned2019-12-06T19:31:21Z-
dc.date.available2013-12-05T02:57:03Zen
dc.date.available2019-12-06T19:31:21Z-
dc.date.copyright2013en
dc.date.issued2013en
dc.identifier.citationLian, H. (2013). Adaptive rates of contraction of posterior distributions in Bayesian wavelet regression. Journal of statistical planning and inference, in press.en
dc.identifier.issn0378-3758en
dc.identifier.urihttps://hdl.handle.net/10356/96486-
dc.identifier.urihttp://hdl.handle.net/10220/18070en
dc.description.abstractIn the last decade, many authors studied asymptotic optimality of Bayesian wavelet estimators such as the posterior median and the posterior mean. In this paper, we consider contraction rates of the posterior distribution in Bayesian wavelet regression in L2/l2 neighborhood of the true parameter, which lies in some Besov space. Using the common spike-and-slab-type of prior with a point mass at zero mixed with a Gaussian distribution, we show that near-optimal rates (that is optimal up to extra logarithmic terms) can be obtained. However, to achieve this, we require that the ratio between the log-variance of the Gaussian prior component and the resolution level is not constant over different resolution levels. Furthermore, we show that by putting a hyperprior on this ratio, the approach is adaptive in that knowledge of the value of the smoothness parameter is no longer necessary. We also discuss possible extensions to other priors such as the sieve prior.en
dc.language.isoenen
dc.relation.ispartofseriesJournal of statistical planning and inferenceen
dc.subjectDRNTU::Science::Mathematics::Applied mathematicsen
dc.titleAdaptive rates of contraction of posterior distributions in Bayesian wavelet regressionen
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen
dc.identifier.doi10.1016/j.jspi.2013.09.002en
item.fulltextNo Fulltext-
item.grantfulltextnone-
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