Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Confidence Sets for Nonparametric Wavelet Regression

Publication Date

September, 2002

Publication Type

Tech Report

Author(s)

Christopher R. Genovese and Larry Wasserman

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.