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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.

MSC:
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
Software:
Healpix
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