Dans cette Note nous présentons une loi du logarithme uniforme pour un estimateur non paramétrique de la régression en présence de données censurées. Cette loi est analogue à celle obtenue, notamment, par Einmahl et Mason [U. Einmahl, D.M. Mason, J. Theor. Probab. 13 (2000) 1–3] dans le cas non censuré.
In this Note, a uniform law of the logarithm is established for a nonparametric estimate of the regression function under random censorship. This law is analogous to that obtained by Einmahl and Mason [U. Einmahl, D.M. Mason, J. Theor. Probab. 13 (2000) 1–3] in the uncensored case.
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@article{CRMATH_2008__346_3-4_225_0,
author = {Vivian Viallon},
title = {Loi du logarithme uniforme pour un estimateur non param\'etrique de la r\'egression en donn\'ees censur\'ees},
journal = {Comptes Rendus. Math\'ematique},
pages = {225--228},
publisher = {Elsevier},
volume = {346},
number = {3-4},
year = {2008},
doi = {10.1016/j.crma.2007.11.030},
language = {fr},
}
TY - JOUR AU - Vivian Viallon TI - Loi du logarithme uniforme pour un estimateur non paramétrique de la régression en données censurées JO - Comptes Rendus. Mathématique PY - 2008 SP - 225 EP - 228 VL - 346 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2007.11.030 LA - fr ID - CRMATH_2008__346_3-4_225_0 ER -
Vivian Viallon. Loi du logarithme uniforme pour un estimateur non paramétrique de la régression en données censurées. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 225-228. doi : 10.1016/j.crma.2007.11.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.030/
[1] Nonparametric, multidimensional estimation of regression derivatives, C. R. Acad. Sci. Paris Ser. I, Volume 339 (2004) no. 10, pp. 713-716
[2] Partitioning-estimates of a regression function under random censoring, Statist. Decisions, Volume 13 (1995) no. 1, pp. 21-37
[3] On the rate of uniform convergence of the Product-Limit estimator: strong and weak laws, Ann. Statist., Volume 25 (1997) no. 3, pp. 1050-1087
[4] Uniform consistency for conditional lifetime distribution estimators under random right-censorship (J.-L. Auget; N. Balakrishnan; M. Mesbah; G. Molenberghs, eds.), Advances in Statistical Methods in the Health Sciences, Applications to Cancer and AIDS Studies, Genome Sequence Analysis and Survival Analysis, Birkhäuser, Boston, 2007, pp. 195-209 (ISBN: 0-8176-4368-0)
[5] General confidence bounds for nonparametric functional estimators, Stat. Inference Stoch. Process., Volume 7 (2004), pp. 225-277
[6] An empirical process approach to the uniform consistency of kernel type estimators, J. Theor. Probab., Volume 13 (2000), pp. 1-13
[7] Uniform in bandwidth consistency of kernel-type function estimators, Ann. Stat., Volume 33 (2005) no. 3, pp. 1380-1403
[8] A LIL type result for the product-limit estimator, Z. Wahrsch. Verw. Gebiete, Volume 56 (1981), pp. 75-86
[9] Nonparametric estimation and regression analysis with left-truncated and right-censored data, J. Am. Stat. Assoc., Volume 91 (1996) no. 426, pp. 1166-1180
[10] Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncation, Ann. Probab., Volume 18 (1990), pp. 160-189
[11] Nonparametric estimation from incomplete observations, J. Am. Stat. Assoc., Volume 53 (1958), pp. 457-481
[12] Prediction from randomly right censored data, J. Multivar. Anal., Volume 80 (2002) no. 1, pp. 73-100
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