Subsampling needlet coefficients on the sphere

Details Subsampling needlet coefficients on the sphere Subsampling needlet coefficients on the sphere

2007-06-28

arxiv.org/abs/0706.4169v2

Bernoulli 2009, Vol. 15, No. 2, 438-463

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ164 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ164

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological data. In the present work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics evaluated on Voronoi cells on the sphere. We illustrate how such statistics can be used for isotropy tests and for bootstrap estimation of nuisance parameters, even when a single realization of the spherical random field is observed. The asymptotic theory is developed in detail in the high resolution sense.

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