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},
     zbl = {0974.62030},
     mrnumber = {1876841},
     language = {en},
     url = {www.numdam.org/item/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://www.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 400529 | Zbl 0331.62030

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

[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 1725709 | Zbl 1054.62589

[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 458674 | Zbl 0283.62023

[5] S Csörgő, Universal Gaussian approximations under random censorship, Ann. Statist. 24 (1996) 2744-2778. | MR 1425977 | Zbl 0868.62042

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

[7] S Diehl, W Stute, Kernel density and hazard function estimation in the presence of censoring, J. Multivariate Anal. 25 (1988) 299-310. | MR 940545 | Zbl 0661.62028

[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 1744994 | Zbl 0995.62042

[9] E Giné, A Guillou, Laws of the iterated logarithm for censored data, Ann. Probab. 27 (1999) 2042-2067. | MR 1742901 | Zbl 0984.62023

[10] E.L Kaplan, P Meier, Non-parametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958) 457-481. | MR 93867 | Zbl 0089.14801

[11] 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

[12] 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

[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 1309627 | Zbl 0815.62016

[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