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High-frequency tail index estimation by nearly tight frames. (English) Zbl 1322.62217

Mayeli, Azita (ed.) et al., Commutative and noncommutative harmonic analysis and applications. AMS special session in memory of Daryl Geller on wavelet and frame theoretic methods in harmonic analysis and partial differential equations, Rochester, NY, USA, September 22–23, 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-9493-4/pbk; 978-1-4704-1106-0/ebook). Contemporary Mathematics 603, 149-187 (2013).
Summary: This work develops the asymptotic properties (weak consistency and Gaussianity), in the high-frequency limit, of approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. The procedure we used exploits the so-called Mexican needlet construction by D. Geller and A. Mayeli [Math. Z. 263, No. 2, 235–264 (2009; Zbl 1193.42124)]. Furthermore, we propose a plug-in procedure to optimize the precision of the estimators in terms of asymptotic variance.
For the entire collection see [Zbl 1278.00026].

MSC:

62M15 Inference from stochastic processes and spectral analysis
62M30 Inference from spatial processes
62F12 Asymptotic properties of parametric estimators
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42C15 General harmonic expansions, frames
62M40 Random fields; image analysis
60G60 Random fields

Citations:

Zbl 1193.42124
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