Asymptotics for spherical needlets

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotictheory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets. 1. Introduction. Over the last two decades, wavelets have emerged as one of the most interesting tools of statistical investigation. In this paper we give an application to the statistical analysis of data sets indexed by the unit sphere S 2 . This is motivated mostly by the analysis of the Cosmic