Spin needlets spectral estimation*

Electronic Journal of Statistics

Volumn 3, Issue , 2009, Pages 1497-1530

  Geller, Daryl ^a   Lan, Xiaohong ^b   Marinucci, Domenico ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Angular power spectrum estimation; Cmb polarization; Fibre bundles; Spin needlets; Spin random fields

Indexed keywords

EID: 78149409538     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-EJS448     Document Type: Article

References (60)

1. Adler, R.J. and Taylor, J.E. (2007) Random Fields and Geometry, Springer.
2. Anderes, E. and Chatterjee, S. (2009), Consistent Estimates of De-formed Isotropic Gaussian Random Fields on the Plane, Annals of Statistics, Vol. 37, No. 5A, pp. 2324-2350.
3. Antoine, J.-P. and Vandergheynst, P. (1999) Wavelets on the Sphere: a Group-Theoretic Approach, Applied and Computational Harmonic Analysis, 7, pp. 262-291.
4. Antoine, J.-P., Demanet, L., Jacques, L., Vandergheynst, P. (2002) Wavelets on the Sphere: Implementation and Approximations, Applied and Computational Harmonic Analysis, 13, 177-200.
5. Antoine, J.-P. and Vandergheynst, P. (2007) Wavelets on the Sphere and Other Conic Sections, Journal of Fourier Analysis and its Applications, 13, 369-386.
6. Baldi, P., Kerkyacharian, G., Marinucci, D. and Picard, D. (2009) Besov Spaces for Sections of Spin Fiber Bundles on the Sphere, preprint.
7. Baldi, P., Kerkyacharian, G., Marinucci, D. and Picard, D. (2009) Asymptotics for Spherical Needlets, Annals of Statistics, Vol. 37, No. 3, 1150-1171.
8. Baldi, P., Kerkyacharian, G., Marinucci, D. and Picard, D. (2009) Subsampling Needlet Coefficients on the Sphere, Bernoulli, Vol. 15, 438-463.
9. Bishop, R.L. and Goldberg, S.I. (1980) Tensor Analysis on Manifolds. Dover Publications, Inc. New York.
10. Bridles, S. et al. (2009) Handbook for the GREAT08 Challenge: an Image Analysis Competition for Gravitational Lensing, Annals of Applied Statistics, Vol. 2, pp. 6-37.
11. Brocker, T., and Tom Dieck, T. (1985) Representations of compact Lie groups, Graduate Texts in Mathematics, 98, Springer-Verlag, New York.
12. Cabella, P. and Kamionkowski, M. (2005) Theory of Cosmic Microwave Background Polarization, arXiv: astro-ph/0403392v2 18 Mar 2005.
13. Cabella, P. and Marinucci, D. (2009) Statistical Challenges in the Analysis of Cosmic Microwave Background Radiation, Annals of Applied Statistics, Vol. 2, pp. 61-95.
14. Delabrouille, J., Cardoso, J.-F., Le Jeune, M., Betoule, M., Fay, G., Guilloux, F. (2008) A Full Sky, Low Foreground, High Resolution CMB Map from WMAP, Astronomy and Astrophysics, Volume 493, Issue 3, 2009, pp. 835-857.
15. Dodelson, S. (2003) Modern Cosmology, Academic Press.
16. Eastwood, M., Tod, P. (1982) Edth-a Differential Operator on the Sphere, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 92, pp. 317-330.
17. Faraut, J. (2008) Analysis of Lie Groups, Cambridge University Press, Cambridge.
18. Faÿ, G. and Guilloux, F. (2008) Consistency of a Needlet Spectral Estimator on the Sphere.
19. Faÿ, G., Guilloux, F., Betoule, M., Cardoso, J.-F., Delabrouille, J., Le Jeune, M. (2008) CMB Power Spectrum Estimation Using Wavelets, Physical Review D, D78:083013.
20. Geller, D., Hansen, F.K., Marinucci, D., Kerkyacharian, G. and Picard, D. (2008) Spin Needlets for Cosmic Microwave Background Polarization Data Analysis, Physical Review D, D78:123533.
21. Geller, D. and Marinucci, D. (2008) Spin Wavelets on the Sphere, preprint.
22. Geller, D. and Mayeli, A. (2009) Continuous wavelets on manifolds, Math. Z., Vol. 262, pp. 895-927.
23. Geller, D. and Mayeli, A. (2009) Nearly tight trames and space-frequency analysis on compact manifolds, Math. Z., Vol. 263 (2009), pp. 235-264.
24. Geller, D. and Mayeli, A. (2009) Besov spaces and frames on compact manifolds, Indiana Univ. Math. J., Vol. 58, pp. 2003-2042.
25. Geller, D. and Mayeli, A. (2009) Nearly tight frames of spin wavelets on the sphere, preprint.
26. Gorski, K.M., Lilje, P.B. (2006) Foreground Subtraction of Cosmic Microwave Background Maps using WI-FIT (Wavelet based hIgh resolution Fitting of Internal Templates), Astrophysical Journal, Vol. 648, 784-796.
27. Guilloux, F., Fay, G., Cardoso, J.-F. (2009) Practical Wavelet Design on the Sphere, Applied and Computational Harmonic Analysis, Vol. 26, pp. 143-160.
28. Goldberg, J.N., Newman, E.T. (1967) Spin-s Spherical Harmonics and ð. Journal of Mathematical Physics, Vol. 8, No. 11, pp. 2155-2166.
29. Gorski, K.M., Hivon, E., Banday, A.J., Wandelt, B.D., Hansen, F.K., Reinecke, M., Bartelman, M. (2005) HEALPix-a Frame-work for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere, Astrophysical Journal 622, 759-771.
30. Jansson, S. (1997) Gaussian Hilbert Spaces, Cambridge University Press.
31. Kamionkowski, M., Kosowski, A., and Stebbins, A. (1996) Statistics of Cosmic Microwave Background Polarization, Physical Review D, Vol. 55, Issue 12, pp. 7468-7388.
32. Lan, X. and Marinucci, D. (2008) The Needlets Bispectrum, Electronic Journal of Statistics, Vol. 2, pp. 332-367.
33. Lan, X. and Marinucci, D. (2009) On the Dependence Structure of Wavelet Coefficients for Spherical Random Fields, Stochastic Processes and their Applications, 119, 3749-3766.
34. Malyarenko, A. (2009) Invariant Random Fields in Vector Bundles and Applications to Cosmology.
35. Marinucci, D. (2006) High-Resolution Asymptotics for the Angular Bispectrum of Spherical Random Fields, The Annals of Statistics, Vol. 34, pp. 1-41.
36. Marinucci, D. (2008) A Central Limit Theorem and Higher Order Results for the Angular Bispectrum, Probability Theory and Related Fields, 141, pp. 389-409.
37. Marinucci, D., Pietrobon, D., Balbi, A., Baldi, P., Cabella, P., Kerkyacharian, G., Natoli, P. Picard, D., Vittorio, N. (2008) Spherical Needlets for CMB Data Analysis, Monthly Notices of the Royal Astronomical Society, Volume 383, Issue 2, pp. 539-545, January 2008.
38. Marinucci, D. and Peccati, G. (2010) Representations of SO(3) and Angular Polyspectra, Journal of Multivariate Analysis, 101, 77-100.
39. Mayeli, A. (2010) Asymptotic Uncorrelation for Mexican Needlets, J. Math. Anal. Appl. Vol. 363, Issue 1, pp. 336-344.
40. McEwen, J.D. (2008) Fast, Exact (but Unstable) Spin Spherical Harmonic Transforms.
41. Narcowich, F.J., Petrushev, P. and Ward, J.D. (2006a) Localized Tight Frames on Spheres, SIAM Journal of Mathematical Analysis Vol. 38, pp. 574-594.
42. Narcowich, F.J., Petrushev, P. and Ward, J.D. (2006b) Decom-position of Besov and Triebel-Lizorkin Spaces on the Sphere, Journal of Functional Analysis, Vol. 238, 2, 530-564.
43. Newman, E.T., Penrose, R. (1966) Note on the Bondi-Metzner-Sachs Group, Journal of Mathematical Physics, Vol. 7 No. 5, 863-870.
44. Nourdin, I., Peccati, G., Reveillac, A. (2008) Multivariate Normal Approximations Using Stein’s Methods and Malliavin Calculus, Annales Institute Henri Poincare’, Probabilites et Statistique, in press.
45. Nualart, D., Peccati, G. (2005) Central Limit Theorems For Sequences of Multiple Stochastic Integrals, Annals of Probability, Vol. 33, pp. 177-193.
46. Peccati, G., and Taqqu, M S. (2008) Moments, cumulants and diagram formulae for non-linear functionals of random measures, preprint.
47. Pietrobon, D., Balbi, A., Marinucci, D. (2006) Integrated Sachs-Wolfe Effect from the Cross Correlation of WMAP3 Year and the NRAO VLA Sky Survey Data: New Results and Constraints on Dark Energy, Physical Review D, id. D:74, 043524.
48. Pietrobon, D., Amblard, A., Balbi, A., Cabella, P., Cooray, A., Marinucci, D. (2008) Needlet Detection of Features in WMAP CMB Sky and the Impact on Anisotropies and Hemispherical Asymmetries, Physical Review D, D78 103504.
49. Pietrobon, D., Cabella, P., Balbi, A., de Gasperis, G., Vittorio, N. (2008) Constraints on Primordial non-Gaussianity from a Needlet Analysis of the WMAP-5 Data.
50. Pietrobon, D., Cabella, P., Balbi, A., Crittenden, R., de Gasperis, G., Vittorio, N. (2009) Needlet Bispectrum Asymmetries in the WMAP5-Year Data.
51. Polenta, G., Marinucci, D., Balbi, A., de Bernardis, P., Hivon, E., Masi, S., Natoli, P., Vittorio, N. (2005) Unbiased estimation of Angular Power Spectra, Journal of Cosmology and Astroparticle Physics, Issue 11, n. 1.
52. Rudjord, O., Hansen, F.K., Lan, X., Liguori, M., Marinucci, D., Matarrese, S. (2009a) An Estimate of the Primordial Non-Gaussianity Parameter fN L Using the Needlet Bispectrum from WMAP, Astrophysical Journal, 701, 369-376.
53. Rudjord, O., Hansen, F.K., Lan, X., Liguori, M., Marinucci, D., Matarrese, S. (2009b) Directional Variations of the Non-Gaussianity Parameter fN L.
54. Schwartzman, A., Mascarenhas, W.F., Taylor, J.E. (2008) Infer-ence for Eigenvalues and Eigenvectors of Gaussian Symmetric Matrices, Annals of Statistics, Vol. 36, pp. 2886-2919.
55. Seljak, U. and Zaldarriaga, M. (1997) An allsky analysis of polarization in the microwave background, Physical Review D, Vol. 55, N. 4, 1830-1840.
56. 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.
57. Varshalovich, D.A., Moskalev, A.N. and Khersonskii, V.K. (1988) Quantum Theory of Angular Momentum. World Scientific, Singapore.
58. Vilenkin, N.Ja. and Klimyk, A.U. (1991) Representation of Lie Groups and Special Functions, Kluwer, Dordrecht.
59. Wiaux, Y., Jacques, L., Vandergheynst, P. (2007) Fast spin ±2 spherical harmonics and applications in cosmology, Journal of Computational Physics, Vol. 226, p. 2359-2371.
60. Wiaux, Y., McEwen, J.D., Vielva, P. (2007) Complex Data Process-ing: Fast Wavelet Analysis on the Sphere, Journal of Fourier Analysis and its Applications, Vol. 13, pp. 477-494.