We construct nonparametric confidence sets for regression functions
using wavelets. 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 functional of
the regression curve.
Keywords: Confidence sets, Stein's unbiased risk estimator,
nonparametric regression, thresholding, wavelets