Rates of strong uniform consistency for multivariate kernel density estimators

Evarist Giné; Armelle Guillou

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 6, page 907-921
  • ISSN: 0246-0203

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Giné, Evarist, and Guillou, Armelle. "Rates of strong uniform consistency for multivariate kernel density estimators." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 907-921. <http://eudml.org/doc/77748>.

@article{Giné2002,
author = {Giné, Evarist, Guillou, Armelle},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {uniformly almost sure rates; kernel density estimators; general upper bound; exact bound},
language = {eng},
number = {6},
pages = {907-921},
publisher = {Elsevier},
title = {Rates of strong uniform consistency for multivariate kernel density estimators},
url = {http://eudml.org/doc/77748},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Giné, Evarist
AU - Guillou, Armelle
TI - Rates of strong uniform consistency for multivariate kernel density estimators
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 907
EP - 921
LA - eng
KW - uniformly almost sure rates; kernel density estimators; general upper bound; exact bound
UR - http://eudml.org/doc/77748
ER -

References

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  7. [7] E. Giné, A. Guillou, On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals, Ann. Inst. Henri Poincaré – PR37 (2001) 503-522. Zbl0974.62030
  8. [8] E. Giné, V.I. Koltchinskii, J. Zinn, Weighted uniform consistency of kernel density estimators, Preprint, 2001. Zbl1052.62034
  9. [9] P. Massart, Rates of convergence in the central limit theorem for empirical processes, Ann. Inst. Henri Poincaré22 (1986) 381-423. Zbl0615.60032MR871904
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  11. [11] D. Nolan, D. Pollard, U-processes: rates of convergence, Ann. Statist.15 (1987) 780-799. Zbl0624.60048MR888439
  12. [12] M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist.27 (1956) 832-835. Zbl0073.14602MR79873
  13. [13] B.W. Silverman, Weak and strong uniform consistency of the kernel estimate of a density and its derivatives, Ann. Statist.6 (1978) 177-189. Zbl0376.62024MR471166
  14. [14] W. Stute, The oscillation behavior of empirical processes: the multivariate case, Ann. Probab.12 (1984) 361-379. Zbl0533.62037MR735843
  15. [15] M. Talagrand, Sharper bounds for Gaussian and empirical processes, Ann. Probab.22 (1994) 28-76. Zbl0798.60051MR1258865
  16. [16] M. Talagrand, New concentration inequalities in product spaces, Invent. Math.126 (1996) 505-563. Zbl0893.60001MR1419006

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