Rates of strong uniform consistency for multivariate kernel density estimators
Giné, Evarist ; Guillou, Armelle
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 907-921 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2002-01-01
@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},
     volume = {38},
     year = {2002},
     pages = {907-921},
     mrnumber = {1955344},
     zbl = {1011.62034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 907-921. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_6_907_0/

[1] K. Alexander, Probability inequalities for empirical processes and a law of iterated logarithm, Ann. Probab. 12 (1984) 1041-1067. | MR 757769 | Zbl 0549.60024

[2] P. Deheuvels, Uniform limit laws for kernel density estimators on possibly unbounded intervals, in: Limnios N., Nikulin M. (Eds.), Recent Advances in Reliability Theory: Methodology, Practice and Inference, Birkhauser, Boston, 2000, pp. 477-492. | MR 1783500 | Zbl 0997.62038

[3] V. De La Peña, E. Giné, Decoupling, from Dependence to Independence, Springer-Verlag, New York, 1999. | MR 1666908 | Zbl 0918.60021

[4] R.M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, Cambridge, UK, 1999. | MR 1720712 | Zbl 0951.60033

[5] U. Einmahl, D. Mason, Some universal results on the behavior of increments of partial sums, Ann. Probab. 24 (1996) 1388-1407. | MR 1411499 | Zbl 0872.60022

[6] U. Einmahl, D. Mason, An empirical process approach to the uniform consistency of kernel-type function estimators, J. Theoret. Probab. 13 (2000) 1-37. | MR 1744994 | Zbl 0995.62042

[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 - PR 37 (2001) 503-522. | Numdam | Zbl 0974.62030

[8] E. Giné, V.I. Koltchinskii, J. Zinn, Weighted uniform consistency of kernel density estimators, Preprint, 2001.

[9] P. Massart, Rates of convergence in the central limit theorem for empirical processes, Ann. Inst. Henri Poincaré 22 (1986) 381-423. | Numdam | MR 871904 | Zbl 0615.60032

[10] S.J. Montgomery-Smith, Comparison of sums of independent identically distributed random vectors, Probab. Math. Statist. 14 (1993) 281-285. | MR 1321767 | Zbl 0827.60005

[11] D. Nolan, D. Pollard, U-processes: rates of convergence, Ann. Statist. 15 (1987) 780-799. | MR 888439 | Zbl 0624.60048

[12] M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. 27 (1956) 832-835. | MR 79873 | Zbl 0073.14602

[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. | MR 471166 | Zbl 0376.62024

[14] W. Stute, The oscillation behavior of empirical processes: the multivariate case, Ann. Probab. 12 (1984) 361-379. | MR 735843 | Zbl 0533.62037

[15] M. Talagrand, Sharper bounds for Gaussian and empirical processes, Ann. Probab. 22 (1994) 28-76. | MR 1258865 | Zbl 0798.60051

[16] M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505-563. | MR 1419006 | Zbl 0893.60001