ADAPTIVE DENSITY ESTIMATION FOR DIRECTIONAL DATA USING NEEDLETS

被引：41

作者：

Baldi, P. ^{[1
]}

Kerkyacharian, G. ^{[2
]}

Marinucci, D. ^{[1
]}

Picard, D. ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00161 Rome, Italy

[2] Lab Probabilites & Modeles Aleatoires, F-75251 Paris 05, France

[3] Univ Paris Diderot, CNRS, LPMA, F-75013 Paris, France

来源：

ANNALS OF STATISTICS | 2009年 / 37卷 / 6A期

关键词：

Density estimation; spherical and directional data; thresholding; needlets; STRONG UNIFORM-CONVERGENCE; ASYMPTOTIC MINIMAX RISK; RIEMANNIAN-MANIFOLDS; SPHERICAL DATA; SPHERES;

D O I：

10.1214/09-AOS682

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：

This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called needlets. We establish a minimax result and prove its optimality. We are motivated by astrophysical applications, in particular in connection with the analysis of ultra high-energy cosmic rays.

引用

页码：3362 / 3395

页数：34

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