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Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields

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Abstract

The aim of this paper is to establish rates of convergence to Gaussianity for wavelet coefficients on circular Poisson random fields. This result is established by using the Stein–Malliavin techniques introduced by Peccati and Zheng (Electron J Probab 15(48):1487–1527, 2010) and the concentration properties of so-called Mexican needlets on the circle.

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Acknowledgments

The author whishes to thank D. Marinucci for the useful discussions and E. Calfa for the accurate reading.

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Authors and Affiliations

  1. University of Tor Vergata, Rome, Italy

    Claudio Durastanti

  2. Ruhr University, Bochum, Germany

    Claudio Durastanti

Authors
  1. Claudio Durastanti
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Correspondence to Claudio Durastanti.

Additional information

This research is partially supported by European Research Council Grant No. 277742 PASCAL and by DFG-GRK 2131.

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Durastanti, C. Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields. Stat Methods Appl 25, 651–673 (2016). https://doi.org/10.1007/s10260-016-0352-0

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