Confidence Sets for Nonparametric Wavelet Regression

<p>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.</p>