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Signal processing methods for EEG data classification
Imperial Users onl
Adaptive nonparametric confidence sets
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.Comment: 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
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