Confidence Sets for Nonparametric Wavelet Regression

Abstract

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.