The Annals of Statistics

Confidence sets for nonparametric wavelet regression

Christopher R. Genovese and Larry Wasserman

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 26 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1117114334

Digital Object Identifier
doi:10.1214/009053605000000011

Mathematical Reviews number (MathSciNet)
MR2163157

Zentralblatt MATH identifier
1068.62057

Subjects
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

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

Citation

Genovese, Christopher R.; Wasserman, Larry. Confidence sets for nonparametric wavelet regression. Ann. Statist. 33 (2005), no. 2, 698--729. doi:10.1214/009053605000000011. https://projecteuclid.org/euclid.aos/1117114334


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