Asymptotics for spherical needlets

Annals of Statistics

Volumn 37, Issue 3, 2009, Pages 1150-1171

  Baldi, P ^a   Kerkyacharian, G ^a,b   Marinucci, D ^a   Picard, D ^a,b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

Central limit theorem; High frequency asymptotics; Random fields; Spherical needlets; Tests for Gaussianity and isotropy

Indexed keywords

EID: 67549149713     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS601     Document Type: Article

References (21)

1. ANGERS, J.-F. and KIM, P. (2005). Multivariate Bayesian function estimation. Ann. Statist. 332967-2999. MR2253110
2. ANTOINE, J.-P. and VANDERGHEYNST, P. (1999). Wavelets on the 2-sphere: A group-theoretical approach. Appl. Comput. Harmon. Anal. 7 262-291. MR1721807
3. ANTOINE, J.-P., DEMANET, L., JACQUES, L. and VANDERGHEYNST, P. (2002). Wavelets on the sphere: Implementation and approximations. Appl. Comput. Harmon. Anal. 13 177-200. MR1942741
4. BALDI, P., KERKYACHARIAN, G., MARINUCCI, D. and PICARD, D. (2008). High-frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the Torus. J. Multivariate Anal. 99 606-636. MR2406074
5. DETTE, H., MELAS, V. B. and PEPELYSHEV, A. (2005). Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors. Ann. Statist. 33 2758-2788. MR2253101
6. DRYDEN, I. L. (2005). Statistical analysis on high-dimensional spheres and shape spaces. Ann. Statist. 33 1643-1665. MR2166558
7. GENOVESE, C. R., MILLER, C. J., NICHOL, R. C., ARJUNWADKAR, M. and WASSERMAN, L. (2004a). Nonparametric inference for the cosmic microwave background. Statist. Sci. 19308-321. MR2146946
8. GENOVESE, C. R.,WASSERMAN, L. and CASELLA, G. (2004b). Introduction to the special section on astrostatistics. Statist. Sci. 19 264. MR2140541
9. GÓRSKI, K. M., HIVON, E., BANDAY, A. J., WANDELT, B. D., HANSEN, F. K., REINECKE, M. and BARTELMANN, M. (2005). HEALPix: A Framework for high-resolution discretization and fast analysis of data distributed on the sphere. Astrophys. J. 622 759-771.
10. GUILLOUX, F., FAY, G. and CARDOSO, J.-F. (2007). Practical wavelet design on the sphere. arxiv:0706.2598v1. Submitted.
11. KERKYACHARIAN, G., PETRUSHEV, P., PICARD, D. and WILLER, T. (2007). Needlet algorithms for estimation in inverse problems. Electron. J. Statist. 1 30-76. MR2312145
12. MARDIA, K. V. and PATRANGENARU, V. (2005). Directions and projective shapes. Ann. Statist. 331666-1699. MR2166559
13. MARINUCCI, D. (2004). Testing for non-Gaussianity on cosmic microwave background radiation: A review. Statist. Sci. 19 294-307. MR2140543
14. MARINUCCI, D. (2006). High-resolution asymptotics for the angular bispectrum of spherical random fields. Ann. Statist. 34 1-41. MR2275233
15. MARINUCCI, D., PIETROBON, D., BALBI, A., BALDI, P., CABELLA, P., KERKYACHARIAN, G., NATOLI, P., PICARD, D. and VITTORIO, N. (2008). Spherical needlets for cosmic microwave background data analysis. Monthly Notices Roy. Astronom. Soc. 383 539-545.
16. NARCOWICH, F. J., PETRUSHEV, P. and WARD, J. D. (2006). Localized tight frames on spheres. SIAM J. Math. Anal. 38 574-594. MR2237162
17. NUALART, D. and PECCATI, G. (2005). Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33 177-193. MR2118863
18. PIETROBON, D., BALBI, A. and MARINUCCI, D. (2006). Integrated Sachs-Wolfe effect from the cross-correlation of WMAP 3 year and NVSS: New results and constraints on dark energy. Phys. Rev. D 74 (043524).
19. STEIN, E. M. and WEISS, G. (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, Princeton, NJ. MR0304972
20. SURGAILIS, D. (2003). CLTs for polynomials of linear sequences: Diagram formula with illustrations. In Theory and Applications of Long-Range Dependence 111-127. Birkhäuser Boston, Boston, MA. MR1956046
21. VARSHALOVICH, D. A.,MOSKALEV, A. N. and KHERSONSKǏI, V. K. (1988). Quantum Theory of Angular Momentum. World Scientific, Teaneck, NJ. MR1022665