U-Statistics on the Spherical Poisson Space

  • Solesne Bourguin
  • Claudio Durastanti
  • Domenico Marinucci
  • Giovanni Peccati
Chapter
Part of the Bocconi & Springer Series book series (BS, volume 7)

Abstract

We review a recent stream of research on normal approximations for linear functionals and more general U-statistics of wavelets/needlets coefficients evaluated on a homogeneous spherical Poisson field. We show how, by exploiting results from Peccati and Zheng (Electron J Probab 15(48):1487–1527, 2010) based on Malliavin calculus and Stein’s method, it is possible to assess the rate of convergence to Gaussianity for a triangular array of statistics with growing dimensions. These results can be exploited in a number of statistical applications, such as spherical density estimations, searching for point sources, estimation of variance, and the spherical two-sample problem.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Solesne Bourguin
    • 1
  • Claudio Durastanti
    • 2
  • Domenico Marinucci
    • 3
  • Giovanni Peccati
    • 4
  1. 1.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  2. 2.Faculty of MathematicsRuhr University BochumBochumGermany
  3. 3.Department of MathematicsUniversity of Rome Tor VergataRomeItaly
  4. 4.Unité de Recherche en MathématiquesUniversité du LuxembourgLuxembourgLuxembourg

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