Adaptive confidence bands

Christopher Genovese; Larry Wasserman

doi:10.1214/07-AOS500

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Home > Journals > Ann. Statist. > Volume 36 > Issue 2 > Article

April 2008 Adaptive confidence bands

Christopher Genovese, Larry Wasserman

Ann. Statist. 36(2): 875-905 (April 2008). DOI: 10.1214/07-AOS500

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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.