Translator Disclaimer
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

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.

Citation

Download Citation

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

Information

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

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

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

Rights: Copyright © 2005 Institute of Mathematical Statistics

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.33 • No. 2 • April 2005
Back to Top