Confidence sets for nonparametric wavelet regression

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We 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.
Published 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)

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Statistics Theory, 62G15 (Primary) 62G99, 62M99, 62E20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/130779

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505632
 http://arxiv.org/abs/math/0505632
 Annals of Statistics 2005, Vol. 33, No. 2, 698-729
 doi:10.1214/009053605000000011

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arXiv