Application of fast spherical Fourier transform to density estimation

DOI10.1016/S0047-259X(02)00041-6zbMath1026.62033MaRDI QIDQ1873106

Harrie Hendriks

Publication date: 19 May 2003

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

Legendre polynomialsoptimal convergence rateband limited functionbox kernelrandomization of grid

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Characteristic functions; other transforms (60E10) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Numerical methods for discrete and fast Fourier transforms (65T50) Applications of functional analysis in probability theory and statistics (46N30)

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Distributions for spherical data based on nonnegative trigonometric sums ⋮ Asymptotic Behavior of the Kernel Density Estimator from a Geometric Viewpoint ⋮ Kernel density estimation on Riemannian manifolds ⋮ Comparison of relative efficiency of kernel density estimator with the exponential map ⋮ Density estimators of Gaussian type on closed Riemannian manifolds ⋮ Nonparametric least squares estimation in derivative families ⋮ Nonparametric recursive regression estimation on Riemannian manifolds ⋮ Adaptive density estimation for directional data using needlets

Cites Work

• Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions
• Optimal rates of convergence for nonparametric estimators
• Spherical deconvolution
• Computing Fourier transforms and convolutions on the 2-sphere
• Aliasing effects and sampling theorems of spherical random fields when sampled on a finite grid
• Optimal global rates of convergence for nonparametric regression
• An empirical Bayes approach to directional data and efficient computation on the sphere
• Unnamed Item