A sharp adaptive confidence ball for self-similar functions

Richard Nickl and Botond Szabó

Stochastic Processes and their Applications, 2016, vol. 126, issue 12, 3913-3934

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.

Keywords: Adaptation; Confidence sets (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2016.04.017

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