Adaptive nonparametric confidence sets

The Annals of Statistics · 2006 · Volume 34 · Issue 1

Abstract

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications include the finite normal mean model, the white noise model, density estimation and regression with random design.

Keywords

62F25, 62G15, 62G20, Adaptation, Density estimation, regression, testing rate, White noise model

Enable JavaScript for citation tools and additional paper interactions.