We consider the correlation structure of the random coefficients for a class of wavelet systems on the sphere (labelled Mexican needlets) which was recently introduced in the literature by [D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Preprint, 2007. arxiv:0706.3642v2]. We provide necessary and sufficient conditions for these coefficients to be asymptotically uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high frequency sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data. (C) 2009 Elsevier B.V. All rights reserved.
Lan, X., Marinucci, D. (2009). On the dependence structure of wavelet coefficients for spherical random fields. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 119(10), 3749-3766 [10.1016/j.spa.2009.07.005].
On the dependence structure of wavelet coefficients for spherical random fields
MARINUCCI, DOMENICO
2009-01-01
Abstract
We consider the correlation structure of the random coefficients for a class of wavelet systems on the sphere (labelled Mexican needlets) which was recently introduced in the literature by [D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Preprint, 2007. arxiv:0706.3642v2]. We provide necessary and sufficient conditions for these coefficients to be asymptotically uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high frequency sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data. (C) 2009 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
