Annals of Statistics

The empirical process on Gaussian spherical harmonics

Domenico Marinucci and Mauro Piccioni

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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.

Article information

Ann. Statist., Volume 32, Number 3 (2004), 1261-1288.

First available in Project Euclid: 24 May 2004

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Primary: 60F17: Functional limit theorems; invariance principles 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions

Empirical processes weak convergence Gaussian spherical harmonics cosmic microwave background radiation


Marinucci, Domenico; Piccioni, Mauro. The empirical process on Gaussian spherical harmonics. Ann. Statist. 32 (2004), no. 3, 1261--1288. doi:10.1214/009053604000000355.

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