A sharp adaptive confidence ball for self-similar functions

Richard Nickl; Botond Szabó

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arXiv · 1406.3994

A sharp adaptive confidence ball for self-similar functions

Richard Nickl·Botond Szabó

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Abstract

In the nonparametric Gaussian sequence space model an $\ell^2$-confidence ball $C_n$ 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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Richard Nickl, Botond Szabó. 2014-06-16. A sharp adaptive confidence ball for self-similar functions. https://arxiv.org/abs/1406.3994

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