Adaptive nonparametric confidence sets

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.

Published at http://dx.doi.org/10.1214/009053605000000877 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Adaptive confidence balls
• Confidence sets for nonparametric wavelet regression
• Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
• Confidence balls in Gaussian regression

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