The empirical process on Gaussian spherical harmonics

Details The empirical process on Gaussian spherical harmonics The empirical process on Gaussian spherical harmonics

2004-06-25

arxiv.org/abs/math/0406526v1

Annals of Statistics 2004, Vol. 32, No. 3, 1261-1288

Mathematics

Statistics Theory

Scientific paper

10.1214/009053604000000355

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation.

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