The empirical process on Gaussian spherical harmonics

• 成果类型: Article
• 署名作者: Marinucci, D; Piccioni, M
• 署名单位: University of Rome Tor Vergata; Sapienza University Rome
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000355
• 发表日期: 2004
• 页码: 1261-1288
• 关键词: microwave; CONVERGENCE; POWER

摘要

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.