Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Adaptive Confidence Bands

Publication Date

January, 2007

Publication Type

Tech Report


Christopher Genovese and Larry Wasserman


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.