Adaptive Confidence Bands

2007/01/18 by Christopher R. Genovese, Larry Wasserman, Genovese, Christopher R. +1 · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Machine Learning and Algorithms #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0701513

openalex publication_date 2007/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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