Directional mixture models and optimal estimation of the mixing density

@inproceedings{Kim1999DirectionalMM,
  title={Directional mixture models and optimal estimation of the mixing density},
  author={Peter T. Kim and Ja-Yong Koo},
  year={1999}
}
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 rotationally invariant densities verifying various smoothness conditions. It is found that the difference in smoothness between the Laplace, the Gaussian and the von Mises-Fisher distributions, lead to contrasting inferential conclusions. 

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