Adaptive nonparametric confidence sets

Details Adaptive nonparametric confidence sets Adaptive nonparametric confidence sets

2006-05-17

arxiv.org/abs/math/0605473v1

Annals of Statistics 2006, Vol. 34, No. 1, 229-253

Mathematics

Statistics Theory

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

Scientific paper

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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