The Annals of Statistics
- Ann. Statist.
- Volume 36, Number 2 (2008), 875-905.
Adaptive confidence bands
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.
Ann. Statist., Volume 36, Number 2 (2008), 875-905.
First available in Project Euclid: 13 March 2008
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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