ADAPTIVE DENSITY ESTIMATION FOR DIRECTIONAL DATA USING NEEDLETS

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...

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Bibliographic Details
Published in:The Annals of statistics 2009-12, Vol.37 (6A), p.3362-3395
Main Authors: Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D.
Format: Article
Language:English
Subjects:
62G07
62G20
65T60
Astrophysics
Correlation coefficients
Cosmic rays
Density
Density estimation
Estimates
Estimators
Exact sciences and technology
General topics
Mathematics
Minimax
Multivariate analysis
needlets
Nonparametric inference
Parametric inference
Polynomials
Probabilities
Probability
Probability and statistics
Sciences and techniques of general use
Spheres
spherical and directional data
Statistics
Statistics Theory
Studies
Threshing
thresholding
Wavelet transforms
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/09-AOS682