Confidence Sets for Nonparametric Wavelet Regression

Christopher R. Genovese and Larry Wasserman


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

Heidi Sestrich 2002-09-05
Here is the full PDF text for this technical report. It is 257458 bytes long.