Adaptive Confidence Bands
Statistics Theory
2007-06-13 v1 Statistics Theory
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^\star 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^\star and construct a procedure that comes within a small constant factor of attaining the lower bound for finite-samples.
Cite
@article{arxiv.math/0701513,
title = {Adaptive Confidence Bands},
author = {Christopher R. Genovese and Larry Wasserman},
journal= {arXiv preprint arXiv:math/0701513},
year = {2007}
}