Electronic Journal of Statistics

The needlets bispectrum

Xiaohong Lan and Domenico Marinucci

Full-text: Open access

Abstract

The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation wavelets on the sphere on the other. To this aim, we introduce the needlets bispectrum and we derive a number of convergence results. Here, the limit theory is developed in the high resolution sense. The leading motivation of these results is the need for statistical procedures for searching non-Gaussianity in Cosmic Microwave Background radiation.

Article information

Source
Electron. J. Statist., Volume 2 (2008), 332-367.

Dates
First available in Project Euclid: 20 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1211317529

Digital Object Identifier
doi:10.1214/08-EJS197

Mathematical Reviews number (MathSciNet)
MR2411439

Zentralblatt MATH identifier
1320.62106

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62M15: Spectral analysis 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60G60: Random fields

Keywords
Bispectrum Needlets Spherical Random Fields Cosmic Microwave Background Radiation High Resolution Asymptotics

Citation

Lan, Xiaohong; Marinucci, Domenico. The needlets bispectrum. Electron. J. Statist. 2 (2008), 332--367. doi:10.1214/08-EJS197. https://projecteuclid.org/euclid.ejs/1211317529


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