Confidence sets for nonparametric wavelet regression

Details Confidence sets for nonparametric wavelet regression Confidence sets for nonparametric wavelet regression

2005-05-30

arxiv.org/abs/math/0505632v1

Annals of Statistics 2005, Vol. 33, No. 2, 698-729

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000011 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000011

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.

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