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April 2008 Adaptive confidence bands
Christopher Genovese, Larry Wasserman
Ann. Statist. 36(2): 875-905 (April 2008). DOI: 10.1214/07-AOS500

Abstract

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f which is close to, but simpler than, f. The surrogate captures the significant features in f. We establish lower bounds on the width for any confidence band for f and construct a procedure that comes within a small constant factor of attaining the lower bound for finite-samples.

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Christopher Genovese. Larry Wasserman. "Adaptive confidence bands." Ann. Statist. 36 (2) 875 - 905, April 2008. https://doi.org/10.1214/07-AOS500

Information

Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1139.62311
MathSciNet: MR2396818
Digital Object Identifier: 10.1214/07-AOS500

Subjects:
Primary: 62G08 , 62G15 , 62G20

Keywords: adaptive confidence sets , lower bounds , Nonparametric confidence bands , Nonparametric regression

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 2 • April 2008
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