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Needlet-Whittle estimates on the unit sphere. (English) Zbl 1337.62287
Summary: We study the asymptotic behaviour of needlets-based approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. We prove consistency and asymptotic Gaussianity, in the high-frequency limit, thus generalizing earlier results by C. Durastanti et al. [J. Multivariate Anal. 104, No. 1, 16–38 (2012; Zbl 1270.62069)] based upon standard Fourier analysis on the sphere. The asymptotic results are then illustrated by an extensive Monte Carlo study.

62M15 Inference from stochastic processes and spectral analysis
62M40 Random fields; image analysis
62G20 Asymptotic properties of nonparametric inference
60G60 Random fields
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
Full Text: DOI Euclid arXiv
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