Confidence sets for nonparametric wavelet regression
Statistics Theory
2007-06-13 v1 Statistics Theory
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.
Cite
@article{arxiv.math/0505632,
title = {Confidence sets for nonparametric wavelet regression},
author = {Christopher R. Genovese and Larry Wasserman},
journal= {arXiv preprint arXiv:math/0505632},
year = {2007}
}
Comments
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)