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On the dependence structure of wavelet coefficients for spherical random fields

Author

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  • Lan, Xiaohong
  • Marinucci, Domenico

Abstract

We consider the correlation structure of the random coefficients for a class of wavelet systems on the sphere (labelled Mexican needlets) which was recently introduced in the literature by [D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Preprint, 2007. arxiv:0706.3642v2]. We provide necessary and sufficient conditions for these coefficients to be asymptotically uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high frequency sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3749-3766
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    Citations

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    Cited by:

    1. Durastanti, Claudio, 2016. "Adaptive global thresholding on the sphere," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 110-132.
    2. Shevchenko, Radomyra & Todino, Anna Paola, 2023. "Asymptotic behaviour of level sets of needlet random fields," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 268-318.
    3. 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.
    4. Lan, Xiaohong & Marinucci, Domenico & Xiao, Yimin, 2018. "Strong local nondeterminism and exact modulus of continuity for spherical Gaussian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1294-1315.

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