The Annals of Statistics

The empirical process on Gaussian spherical harmonics

Domenico Marinucci and Mauro Piccioni

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Abstract

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

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

Dates
First available in Project Euclid: 24 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1085408502

Digital Object Identifier
doi:10.1214/009053604000000355

Mathematical Reviews number (MathSciNet)
MR2065205

Zentralblatt MATH identifier
1051.60035

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

Keywords
Empirical processes weak convergence Gaussian spherical harmonics cosmic microwave background radiation

Citation

Marinucci, Domenico; Piccioni, Mauro. The empirical process on Gaussian spherical harmonics. Ann. Statist. 32 (2004), no. 3, 1261--1288. doi:10.1214/009053604000000355. https://projecteuclid.org/euclid.aos/1085408502


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