On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 4, pp. 503-522.
@article{AIHPB_2001__37_4_503_0,
     author = {Gin\'e, Evarist and Guillou, Armelle},
     title = {On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {503--522},
     publisher = {Elsevier},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1876841},
     zbl = {0974.62030},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2001__37_4_503_0/}
}
TY  - JOUR
AU  - Giné, Evarist
AU  - Guillou, Armelle
TI  - On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2001
SP  - 503
EP  - 522
VL  - 37
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPB_2001__37_4_503_0/
LA  - en
ID  - AIHPB_2001__37_4_503_0
ER  - 
%0 Journal Article
%A Giné, Evarist
%A Guillou, Armelle
%T On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2001
%P 503-522
%V 37
%N 4
%I Elsevier
%U http://archive.numdam.org/item/AIHPB_2001__37_4_503_0/
%G en
%F AIHPB_2001__37_4_503_0
Giné, Evarist; Guillou, Armelle. On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 4, pp. 503-522. http://archive.numdam.org/item/AIHPB_2001__37_4_503_0/

[1] O.O Aalen, Nonparametric inference in connection with multiple decrement models, Scand. J. Statist. 3 (1976) 15-27. | MR | Zbl

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

[3] D Bitouzé, B Laurent, P Massart, A Dvoretzky-Kiefer-Wolfowitz type inequality for the Kaplan-Meier estimator, Ann. Inst. Henri Poincaré 35 (1999) 735-763. | Numdam | MR | Zbl

[4] N Breslow, J Crowley, A large sample study of the life table and product limit estimates under random censorship, Ann. Statist. 2 (1974) 437-453. | MR | Zbl

[5] S Csörgő, Universal Gaussian approximations under random censorship, Ann. Statist. 24 (1996) 2744-2778. | MR | Zbl

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

[7] S Diehl, W Stute, Kernel density and hazard function estimation in the presence of censoring, J. Multivariate Anal. 25 (1988) 299-310. | MR | Zbl

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

[9] E Giné, A Guillou, Laws of the iterated logarithm for censored data, Ann. Probab. 27 (1999) 2042-2067. | MR | Zbl

[10] E.L Kaplan, P Meier, Non-parametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958) 457-481. | MR | Zbl

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

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

[13] W Nelson, Theory and applications of hazard plotting for censored failure data, Technometrics 14 (1972) 945-966.

[14] W Stute, Strong and weak representations of cumulative hazard function and Kaplan-Meier estimators on increasing sets, J. Statist. Plann. Inference 42 (1994) 315-329. | MR | Zbl

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

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