The Annals of Statistics

Adaptive nonparametric confidence sets

James Robins and Aad van der Vaart

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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.

Article information

Ann. Statist., Volume 34, Number 1 (2006), 229-253.

First available in Project Euclid: 2 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G15: Tolerance and confidence regions 62G20: Asymptotic properties 62F25: Tolerance and confidence regions

Adaptation white noise model density estimation regression testing rate


Robins, James; van der Vaart, Aad. Adaptive nonparametric confidence sets. Ann. Statist. 34 (2006), no. 1, 229--253. doi:10.1214/009053605000000877.

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