Confidence sets for nonparametric wavelet regression
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 arXiv:
 arXiv:math/0505632
 Bibcode:
 2005math......5632G
 Keywords:

 Mathematics  Statistics;
 62G15 (Primary) 62G99;
 62M99;
 62E20 (Secondary)
 EPrint:
 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)