Confidence sets for nonparametric wavelet regression
Genovese, Christopher R. ; Wasserman, Larry
Ann. Statist., Tome 33 (2005) no. 1, p. 698-729 / Harvested from Project Euclid
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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.
Publié le : 2005-04-14
Classification:  Confidence sets,  Stein’s unbiased risk estimator,  nonparametric regression,  thresholding,  wavelets,  62G15,  62G99,  62M99,  62E20 
@article{1117114334,
     author = {Genovese, Christopher R. and Wasserman, Larry},
     title = {Confidence sets for nonparametric wavelet regression},
     journal = {Ann. Statist.},
     volume = {33},
     number = {1},
     year = {2005},
     pages = { 698-729},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1117114334}
}

Genovese, Christopher R.; Wasserman, Larry. Confidence sets for nonparametric wavelet regression. Ann. Statist., Tome 33 (2005) no. 1, pp.  698-729. http://gdmltest.u-ga.fr/item/1117114334/