Adaptive Confidence Bands

Christopher R. Genovese; Larry Wasserman

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arXiv · math/0701513

Adaptive Confidence Bands

Christopher R. Genovese·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^\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.

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Christopher R. Genovese, Larry Wasserman. 2007-01-18. Adaptive Confidence Bands. https://arxiv.org/abs/math/0701513

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