The Annals of Statistics

Adaptive density estimation for directional data using needlets

P. Baldi, G. Kerkyacharian, D. Marinucci, and D. Picard

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Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 6A (2009), 3362-3395.

Dates
First available in Project Euclid: 17 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1250515390

Digital Object Identifier
doi:10.1214/09-AOS682

Mathematical Reviews number (MathSciNet)
MR2549563

Zentralblatt MATH identifier
1369.62061

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 65T60: Wavelets

Keywords
Density estimation spherical and directional data thresholding needlets

Citation

Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D. Adaptive density estimation for directional data using needlets. Ann. Statist. 37 (2009), no. 6A, 3362--3395. doi:10.1214/09-AOS682. https://projecteuclid.org/euclid.aos/1250515390


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References

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