Confidence sets for nonparametric wavelet regression

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dc.creatorGenovese, Christopher R.
dc.creatorWasserman, Larry
dc.date2005-05-30
dc.date.accessioned2026-07-07T08:06:57Z
dc.date.available2026-07-07T08:06:57Z
dc.descriptionWe construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by showing that a pivot process, constructed from the loss function, converges uniformly to a mean zero Gaussian process. Inverting this pivot yields a confidence set for the wavelet coefficients, and from this we obtain confidence sets on functionals of the regression curve.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053605000000011 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0505632
dc.identifierhttp://arxiv.org/abs/math/0505632
dc.identifierAnnals of Statistics 2005, Vol. 33, No. 2, 698-729
dc.identifierdoi:10.1214/009053605000000011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130779
dc.subjectStatistics Theory
dc.subject62G15 (Primary) 62G99, 62M99, 62E20 (Secondary)
dc.titleConfidence sets for nonparametric wavelet regression
dc.typetext

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