Spectral estimation on the sphere with needlets: high frequency asymptotics

G. Faÿ 1 F. Guilloux 2, *
* Corresponding author
1 APC - ADAMIS
LPP - Laboratoire Paul Painlevé, APC - UMR 7164 - AstroParticule et Cosmologie, MAS - Mathématiques Appliquées aux Systèmes - EA 4037
2 APC - Adamis
LSTA - Laboratoire de Statistique Théorique et Appliquée, MODAL'X - Modélisation aléatoire de Paris X, LPMA - Laboratoire de Probabilités et Modèles Aléatoires, APC - UMR 7164 - AstroParticule et Cosmologie
Abstract : The angular power spectrum of a stationary random field on the sphere is estimated from the needlet coefficients of a single realization, observed with increasingly fine resolution. The estimator we consider is similar to the one recently used in practice by (Faÿ et al. 2008) to estimate the power spectrum of the Cosmic Microwave Background. The consistency of the estimator, in the asymptotics of high frequencies, is proved for a model with a stationary Gaussian field corrupted by heteroscedastic noise and missing data.
Document type :
Journal articles
Statistical Inference for Stochastic Processes, Springer Verlag (Germany), 2011, 14 (1), pp.1-25. <10.1007/s11203-010-9050-y>


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Submitted on : Monday, November 3, 2008 - 11:02:08 PM
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G. Faÿ, F. Guilloux. Spectral estimation on the sphere with needlets: high frequency asymptotics. Statistical Inference for Stochastic Processes, Springer Verlag (Germany), 2011, 14 (1), pp.1-25. <10.1007/s11203-010-9050-y>. <hal-00296576v2>

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