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Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields. (English) Zbl 1359.60037

Summary: 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 P. Giovanni and C. Zheng [Electron. J. Probab. 15, Paper No. 48, 1487–1527 (2010; Zbl 1228.60031)] and the concentration properties of so-called Mexican needlets on the circle.

MSC:

60F05 Central limit and other weak theorems
60G60 Random fields
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
60H07 Stochastic calculus of variations and the Malliavin calculus
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 1228.60031

Software:

CircStats; circular
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Full Text: DOI arXiv

References:

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