@article{AIHPB_2002__38_6_907_0, author = {Gin\'e, Evarist and Guillou, Armelle}, title = {Rates of strong uniform consistency for multivariate kernel density estimators}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {907--921}, publisher = {Elsevier}, volume = {38}, number = {6}, year = {2002}, mrnumber = {1955344}, zbl = {1011.62034}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_2002__38_6_907_0/} }
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 SP - 907 EP - 921 VL - 38 IS - 6 PB - Elsevier UR - http://archive.numdam.org/item/AIHPB_2002__38_6_907_0/ LA - en ID - AIHPB_2002__38_6_907_0 ER -
%0 Journal Article %A Giné, Evarist %A Guillou, Armelle %T Rates of strong uniform consistency for multivariate kernel density estimators %J Annales de l'I.H.P. Probabilités et statistiques %D 2002 %P 907-921 %V 38 %N 6 %I Elsevier %U http://archive.numdam.org/item/AIHPB_2002__38_6_907_0/ %G en %F AIHPB_2002__38_6_907_0
Giné, Evarist; Guillou, Armelle. Rates of strong uniform consistency for multivariate kernel density estimators. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 6, pp. 907-921. http://archive.numdam.org/item/AIHPB_2002__38_6_907_0/
[1] Probability inequalities for empirical processes and a law of iterated logarithm, Ann. Probab. 12 (1984) 1041-1067. | MR | Zbl
,[2] Uniform limit laws for kernel density estimators on possibly unbounded intervals, in: , (Eds.), Recent Advances in Reliability Theory: Methodology, Practice and Inference, Birkhauser, Boston, 2000, pp. 477-492. | MR | Zbl
,[3] Decoupling, from Dependence to Independence, Springer-Verlag, New York, 1999. | MR | Zbl
, ,[4] Uniform Central Limit Theorems, Cambridge University Press, Cambridge, UK, 1999. | MR | Zbl
,[5] Some universal results on the behavior of increments of partial sums, Ann. Probab. 24 (1996) 1388-1407. | MR | Zbl
, ,[6] An empirical process approach to the uniform consistency of kernel-type function estimators, J. Theoret. Probab. 13 (2000) 1-37. | MR | Zbl
, ,[7] On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals, Ann. Inst. Henri Poincaré - PR 37 (2001) 503-522. | Numdam | Zbl
, ,[8] E. Giné, V.I. Koltchinskii, J. Zinn, Weighted uniform consistency of kernel density estimators, Preprint, 2001.
[9] Rates of convergence in the central limit theorem for empirical processes, Ann. Inst. Henri Poincaré 22 (1986) 381-423. | Numdam | MR | Zbl
,[10] Comparison of sums of independent identically distributed random vectors, Probab. Math. Statist. 14 (1993) 281-285. | MR | Zbl
,[11] U-processes: rates of convergence, Ann. Statist. 15 (1987) 780-799. | MR | Zbl
, ,[12] Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. 27 (1956) 832-835. | MR | Zbl
,[13] Weak and strong uniform consistency of the kernel estimate of a density and its derivatives, Ann. Statist. 6 (1978) 177-189. | MR | Zbl
,[14] The oscillation behavior of empirical processes: the multivariate case, Ann. Probab. 12 (1984) 361-379. | MR | Zbl
,[15] Sharper bounds for Gaussian and empirical processes, Ann. Probab. 22 (1994) 28-76. | MR | Zbl
,[16] New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505-563. | MR | Zbl
,