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

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  • Claudio Durastanti

    (University of Tor Vergata
    Ruhr University)

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.

Suggested Citation

  • Claudio Durastanti, 2016. "Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 651-673, November.
    • Handle: RePEc:spr:stmapp:v:25:y:2016:i:4:d:10.1007_s10260-016-0352-0
    DOI: 10.1007/s10260-016-0352-0
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    References listed on IDEAS

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    1. Durastanti, Claudio & Geller, Daryl & Marinucci, Domenico, 2012. "Adaptive nonparametric regression on spin fiber bundles," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 16-38, February.
    2. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    3. Li, Yongming & Wei, Chengdong & Xing, Guodong, 2011. "Berry-Esseen bounds for wavelet estimator in a regression model with linear process errors," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 103-110, January.
    4. Di Marzio, Marco & Panzera, Agnese & Taylor, Charles C., 2009. "Local polynomial regression for circular predictors," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2066-2075, October.
    5. Christophe Ley & Camille Sabbah & Thomas Verdebout, 2014. "A new concept of quantiles for directional data and the angular Mahalanobis depth," Working Papers ECARES ECARES 2013-23, ULB -- Universite Libre de Bruxelles.
    6. Lan, Xiaohong & Marinucci, Domenico, 2009. "On the dependence structure of wavelet coefficients for spherical random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3749-3766, October.
    7. Wu, Wei-Ying & Lim, Chae Young & Xiao, Yimin, 2013. "Tail estimation of the spectral density for a stationary Gaussian random field," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 74-91.
    8. Klemelä, Jussi, 2000. "Estimation of Densities and Derivatives of Densities with Directional Data," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 18-40, April.
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