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A sharp adaptive confidence ball for self-similar functions

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  • Nickl, Richard
  • Szabó, Botond

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.

Suggested Citation

  • Nickl, Richard & Szabó, Botond, 2016. "A sharp adaptive confidence ball for self-similar functions," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3913-3934.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:12:p:3913-3934
    DOI: 10.1016/j.spa.2016.04.017
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    References listed on IDEAS

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    1. T. Tony Cai & Mark Low & Zongming Ma, 2014. "Adaptive Confidence Bands for Nonparametric Regression Functions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1054-1070, September.
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    Keywords

    Adaptation; Confidence sets;

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