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Minimax nonparametric testing in a problem related to the radon transform

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Abstract

We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are non-adaptive. We also construct a minimax rate-optimal adaptive test of rather simple structure.

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Authors and Affiliations

  1. Dept. of Math. II, St. Petersburg State Electrotechn. Univ., St. Petersburg, Russia

    Yu. I. Ingster

  2. Dept. of Math. and Statist., Univ. of Cyprus, Nicosia, Cyprus

    T. Sapatinas

  3. Dept. of Math, St. Petersburg State Univ. of Inform. Technol., Mech. and Optics, St. Petersburg, Russia

    I. A. Suslina

Authors
  1. Yu. I. Ingster
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  2. T. Sapatinas
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  3. I. A. Suslina
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Correspondence to Yu. I. Ingster.

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Ingster, Y.I., Sapatinas, T. & Suslina, I.A. Minimax nonparametric testing in a problem related to the radon transform. Math. Meth. Stat. 20, 347–364 (2011). https://doi.org/10.3103/S1066530711040041

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  • DOI: https://doi.org/10.3103/S1066530711040041

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