Annals of Statistics

Adaptive confidence bands

Christopher Genovese and Larry Wasserman

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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.

Article information

Source
Ann. Statist., Volume 36, Number 2 (2008), 875-905.

Dates
First available in Project Euclid: 13 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1205420522

Digital Object Identifier
doi:10.1214/07-AOS500

Mathematical Reviews number (MathSciNet)
MR2396818

Zentralblatt MATH identifier
1139.62311

Subjects
Primary: 62G15: Tolerance and confidence regions 62G08: Nonparametric regression 62G20: Asymptotic properties

Keywords
Nonparametric confidence bands nonparametric regression adaptive confidence sets lower bounds

Citation

Genovese, Christopher; Wasserman, Larry. Adaptive confidence bands. Ann. Statist. 36 (2008), no. 2, 875--905. doi:10.1214/07-AOS500. https://projecteuclid.org/euclid.aos/1205420522


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