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February 2006 Adaptive nonparametric confidence sets
James Robins, Aad van der Vaart
Ann. Statist. 34(1): 229-253 (February 2006). DOI: 10.1214/009053605000000877


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.


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James Robins. Aad van der Vaart. "Adaptive nonparametric confidence sets." Ann. Statist. 34 (1) 229 - 253, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62039
MathSciNet: MR2275241
Digital Object Identifier: 10.1214/009053605000000877

Primary: 62F25 , 62G15 , 62G20

Keywords: Adaptation , Density estimation , regression , testing rate , White noise model

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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