Consistency of a needlet spectral estimator on the sphere

Details Consistency of a needlet spectral estimator on the sphere Consistency of a needlet spectral estimator on the sphere

2008-07-14

arxiv.org/abs/0807.2162v1

Mathematics

Statistics Theory

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics

Scientific paper

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 (Fa\"{y} 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.

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