High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus

Details High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus High Frequency Asymptotics for Wavelet-Based Tests for Gaussianity and Isotropy on the Torus

2006-06-07

arxiv.org/abs/math/0606154v2

Journal of Multivariate Analysis, Vol. 99, pp. 606-636 (2008)

Mathematics

Statistics Theory

33 pages, 3 figures

Scientific paper

We prove a CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to observations of a single field which is sampled at higher and higher frequencies. We consider also studentized statistics for the case of an unknown correlation structure. The results are motivated by the analysis of cosmological data or high-frequency financial data sets, with a particular interest towards testing for Gaussianity and isotropy

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