Open Access
April 2005 Confidence sets for nonparametric wavelet regression
Christopher R. Genovese, Larry Wasserman
Ann. Statist. 33(2): 698-729 (April 2005). DOI: 10.1214/009053605000000011


We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. 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 functionals of the regression curve.


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Christopher R. Genovese. Larry Wasserman. "Confidence sets for nonparametric wavelet regression." Ann. Statist. 33 (2) 698 - 729, April 2005.


Published: April 2005
First available in Project Euclid: 26 May 2005

zbMATH: 1068.62057
MathSciNet: MR2163157
Digital Object Identifier: 10.1214/009053605000000011

Primary: 62G15
Secondary: 62E20 , 62G99 , 62M99

Keywords: Confidence sets , Nonparametric regression , Stein’s unbiased risk estimator , thresholding , Wavelets

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 2 • April 2005
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