The Annals of Statistics

Confidence sets for nonparametric wavelet regression

Christopher R. Genovese and Larry Wasserman

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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.

Article information

Ann. Statist., Volume 33, Number 2 (2005), 698-729.

First available in Project Euclid: 26 May 2005

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Zentralblatt MATH identifier

Primary: 62G15: Tolerance and confidence regions
Secondary: 62G99: None of the above, but in this section 62M99: None of the above, but in this section 62E20: Asymptotic distribution theory

Confidence sets Stein’s unbiased risk estimator nonparametric regression thresholding wavelets


Genovese, Christopher R.; Wasserman, Larry. Confidence sets for nonparametric wavelet regression. Ann. Statist. 33 (2005), no. 2, 698--729. doi:10.1214/009053605000000011.

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