Asymptotics for spherical needlets

By P. Baldi, Gerard Kerkyacharian, Domenico Marinucci, Dominique Picard. 2006

135 citations recorded by the source corpus.

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

Subfields: Biomedical Engineering, Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/712266f4e4035b1c6cf6f0631b29aed2778c7396

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

Citations in the corpus

New Berry-Esseen bounds for non-linear functionals of Poisson random measures (2013, background): “ with the Gaussian case have found notable applications in the theory and statistics of Gaussian random processes [3, 4] (most prominently the fractional Brownian motion [15]), spherical random ﬁelds [1, 14], random matrix theory [17] and universality questions [19], whereas the ﬁndings for Poisson ”