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Directional mixture models and optimal estimation of the mixing density
Author(s) -
Kim Peter,
Koo JaYong
Publication year - 2000
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315986
Subject(s) - smoothness , minimax , mixing (physics) , gaussian , mathematics , nonparametric statistics , von mises yield criterion , density estimation , spherical harmonics , convergence (economics) , euclidean geometry , mathematical optimization , mathematical analysis , statistics , estimator , geometry , physics , quantum mechanics , finite element method , thermodynamics , economics , economic growth
The authors develop consistent nonparametric estimation techniques for the directional mixing density. Classical spherical harmonics are used to adapt Euclidean techniques to this directional environment. Minimax rates of convergence are obtained for rotation ally invariant densities verifying various smoothness conditions. It is found that the differences in smoothness between the Laplace, the Gaussian and the von Mises‐Fisher distributions lead to contrasting inferential conclusions.