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An empirical Bayes approach to directional data and efficient computation on the sphere. (English) Zbl 0856.62010

Summary: This paper proposes a consistent nonparametric empirical Bayes estimator of the prior density for directional data. The methodology is to use Fourier analysis on \(S^2\) to adapt Euclidean techniques to this non-Euclidean environment. General consistency results are obtained. In addition, a discussion of efficient numerical computation of Fourier transforms on \(S^2\) is given, and their applications to the methods suggested in this paper are sketched.

MSC:

62C12 Empirical decision procedures; empirical Bayes procedures
62G05 Nonparametric estimation
65T50 Numerical methods for discrete and fast Fourier transforms
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
62H11 Directional data; spatial statistics
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