Uniform convergence of density estimators on spheres

Monique Bertrand-Retali; Larbi Ait-Hennani

Applicationes Mathematicae (1995)

  • Volume: 22, Issue: 4, page 427-446
  • ISSN: 1233-7234

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Bertrand-Retali, Monique, and Ait-Hennani, Larbi. "Uniform convergence of density estimators on spheres." Applicationes Mathematicae 22.4 (1995): 427-446. <http://eudml.org/doc/219105>.

@article{Bertrand1995,
author = {Bertrand-Retali, Monique, Ait-Hennani, Larbi},
journal = {Applicationes Mathematicae},
keywords = {histogram estimator; kernel estimator; spherical cap estimator; uniform convergence theorems},
language = {eng},
number = {4},
pages = {427-446},
title = {Uniform convergence of density estimators on spheres},
url = {http://eudml.org/doc/219105},
volume = {22},
year = {1995},
}

TY - JOUR
AU - Bertrand-Retali, Monique
AU - Ait-Hennani, Larbi
TI - Uniform convergence of density estimators on spheres
JO - Applicationes Mathematicae
PY - 1995
VL - 22
IS - 4
SP - 427
EP - 446
LA - eng
KW - histogram estimator; kernel estimator; spherical cap estimator; uniform convergence theorems
UR - http://eudml.org/doc/219105
ER -

References

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  1. [1] Z. D. Bai, C. Radakrishna Rao and L. C. Zhao, Kernel estimators of density function of directional data, J. Multivariate Anal. 27 (1988), 24-39. Zbl0669.62015
  2. [2] M. Bertrand-Retali, Convergence uniforme stochastique d'un estimateur d'une densité de probabilité dans ℝ^s, C. R. Acad. Sci. Paris Sér. A 278 (1974), 451-453. Zbl0275.62031
  3. [3] M. Bertrand-Retali, Convergence uniforme d'un estimateur de la densité par la méthode du noyau, Rev. Roumaine Math. Pures Appl. 23 (1978), 361-385. Zbl0375.62080
  4. [4] J. Geffroy, Sur l'estimation d'une densité dans un espace métrique, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1449-1452. Zbl0305.62024
  5. [5] P. Hall, G. S. Watson and J. Cabrera, Kernel density estimation with spherical data, Biometrika 74 (1987), 751-762. Zbl0632.62033
  6. [6] F. H. Ruymgaart, Strong uniform convergence of density estimators on spheres, J. Statist. Plann. Inference 23 (1989), 45-52. Zbl0685.62039
  7. [7] G. S. Watson, Statistics on Spheres, University of Arkansas Lecture Notes in Math. Sci., Wiley, 1983. 

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