In the nonparametric Gaussian sequence space model an ℓ2-confidence ball Cn is constructed that adapts to unknown smoothness and Sobolev-norm of the infinite-dimensional parameter to be estimated. The confidence ball has exact and honest asymptotic coverage over appropriately defined ‘self-similar’ parameter spaces. It is shown by information-theoretic methods that this ‘self-similarity’ condition is weakest possible.
A sharp adaptive confidence ball for self-similar functions
Szabo, Botond
2016
Abstract
In the nonparametric Gaussian sequence space model an ℓ2-confidence ball Cn is constructed that adapts to unknown smoothness and Sobolev-norm of the infinite-dimensional parameter to be estimated. The confidence ball has exact and honest asymptotic coverage over appropriately defined ‘self-similar’ parameter spaces. It is shown by information-theoretic methods that this ‘self-similarity’ condition is weakest possible.
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