Spectral estimation on the sphere with needlets: High frequency asymptotics

摘要

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 the one recently used in practice by (Fa? 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.