Spectral estimation on the sphere with needlets: high frequency asymptotics

G. Faÿ (1) , F. Guilloux (1)

1 APC-Gravitation - APC - Gravitation

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.

Mots clés: Spherical random fields; Angular power spectrum estimation; High resolution asymptotics; Spherical wavelets; Needlets; Cosmic Microwave Background

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]

G. Faÿ, F. Guilloux. Spectral estimation on the sphere with needlets: high frequency asymptotics. Statistical Inference for Stochastic Processes, 2011, 14 (1), pp.1-25. ⟨10.1007/s11203-010-9050-y⟩. ⟨hal-00296576v2⟩