ASYMPTOTICS FOR SPHERICAL NEEDLETS

被引:86
作者
Baldi, P. [1 ]
Kerkyacharian, G.
Marinucci, D. [1 ]
Picard, D.
机构
[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00161 Rome, Italy
关键词
High-frequency asymptotics; spherical needlets; random fields; central limit theorem; tests for Gaussianity and isotropy; GAUSSIANITY; WAVELETS; SPHERES;
D O I
10.1214/08-AOS601
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT converaence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.
引用
收藏
页码:1150 / 1171
页数:22
相关论文
共 21 条
[1]   Multivariate Bayesian function estimation [J].
Angers, JF ;
Kim, PT .
ANNALS OF STATISTICS, 2005, 33 (06) :2967-2999
[2]   Wavelets on the sphere: implementation and approximations [J].
Antoine, JP ;
Demanet, L ;
Jacques, L ;
Vandergheynst, P .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2002, 13 (03) :177-200
[3]  
Antoine JP, 1999, APPL COMPUT HARMON A, V7, P262, DOI 10.1006/acha.1998.0272
[4]   High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus [J].
Baldi, Paolo ;
Kerkyacharian, Gerard ;
Marinucci, Domenico ;
Picard, Dominique .
JOURNAL OF MULTIVARIATE ANALYSIS, 2008, 99 (04) :606-636
[5]   Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors [J].
Dette, H ;
Melas, VB ;
Pepelyshev, A .
ANNALS OF STATISTICS, 2005, 33 (06) :2758-2788
[6]   Statistical analysis on high-dimensional spheres and shape spaces [J].
Dryden, IL .
ANNALS OF STATISTICS, 2005, 33 (04) :1643-1665
[7]   Nonparametric inference for the cosmic microwave background [J].
Genovese, CR ;
Miller, CJ ;
Nichol, RC ;
Arjunwadkar, M ;
Wasserman, L .
STATISTICAL SCIENCE, 2004, 19 (02) :308-321
[8]   Introduction to the special section on astrostatistics [J].
Genovese, CR ;
Wasserman, L ;
Casella, G .
STATISTICAL SCIENCE, 2004, 19 (02) :264-264
[9]   HEALPix:: A framework for high-resolution discretization and fast analysis of data distributed on the sphere [J].
Górski, KM ;
Hivon, E ;
Banday, AJ ;
Wandelt, BD ;
Hansen, FK ;
Reinecke, M ;
Bartelmann, M .
ASTROPHYSICAL JOURNAL, 2005, 622 (02) :759-771
[10]  
Guilloux F., 2007, ARXIV07062598V1