Adaptive confidence bands
Christopher Genovese, Larry Wasserman
The Annals of Statistics · 2008 · Volume 36 · Issue 2
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.
Keywords
62G08, 62G15, 62G20, adaptive confidence sets, lower bounds, Nonparametric confidence bands, Nonparametric regression
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