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Maxiset Point of View for Signal Detection in Inverse Problems

Mathematical Methods of Statistics volume 28, pages 228–242 (2019)Cite this article

Abstract

This paper extends the successful maxiset paradigm from function estimation to signal detection in inverse problems. In this context, the maxisets do not have the same shape compared to the classical estimation framework. Nevertheless, we introduce a robust version of these maxisets allowing to exhibit tail conditions on the signals of interest. Under this novel paradigm we are able to compare direct and indirect testing procedures.

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Authors and Affiliations

  1. Inst. de Math. de Marseille, Aix-Marseille Univ., Marseille, France

    F. Autin & J.-M. Freyermuth

  2. Univ. de Lorraine, CNRS, IECL, Nancy, France

    M. Clausel

  3. Inst. Camille Jordan, Univ. Lyon, Univ. Claude Bernard Lyon 1 CNRS UMR 5208, Villeurbanne, France

    C. Marteau

Authors
  1. F. Autin
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  2. M. Clausel
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  3. J.-M. Freyermuth
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  4. C. Marteau
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Corresponding authors

Correspondence to F. Autin, M. Clausel, J.-M. Freyermuth or C. Marteau.

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Autin, F., Clausel, M., Freyermuth, JM. et al. Maxiset Point of View for Signal Detection in Inverse Problems. Math. Meth. Stat. 28, 228–242 (2019). https://doi.org/10.3103/S1066530719030037

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  • DOI: https://doi.org/10.3103/S1066530719030037

Keywords

  • maxiset
  • inverse problems
  • signal detection

AMS 2010 Subject Classification

  • 62G20