Comptes Rendus
no. 13-14
Statistics
A strong consistency of a nonparametric estimate of entropy under random censorship
[Loi du logarithme pour un estimateur non paramétrique de l'entropie en présence de données censurées]

Présenté par : Paul Deheuvels

Salim Bouzebda1 ; Issam Elhattab1
1 L.S.T.A., Université de Paris 6, 175, rue du Chevaleret, bâtiment A, 75013 Paris, France
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 821-826.

Dans cette Note, nous obtenons la consistance forte pour un estimateur non paramétrique de l'entropie en présence de données censurées. Nous montrons que ce résultat demeure valable uniformément en terme de la fenêtre.

The purpose of this Note is to provide the rate of strong consistency for a nonparametric estimator of entropy under random censorship. We also establish an uniform-in-bandwidth consistency for this estimator.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.021
Salim Bouzebda 1 ; Issam Elhattab 1

1 L.S.T.A., Université de Paris 6, 175, rue du Chevaleret, bâtiment A, 75013 Paris, France 
@article{CRMATH_2009__347_13-14_821_0,
     author = {Salim Bouzebda and Issam Elhattab},
     title = {A strong consistency of a nonparametric estimate of entropy under random censorship},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {821--826},
     publisher = {Elsevier},
     volume = {347},
     number = {13-14},
     year = {2009},
     doi = {10.1016/j.crma.2009.04.021},
     language = {en},
}
TY  - JOUR
AU  - Salim Bouzebda
AU  - Issam Elhattab
TI  - A strong consistency of a nonparametric estimate of entropy under random censorship
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 821
EP  - 826
VL  - 347
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2009.04.021
LA  - en
ID  - CRMATH_2009__347_13-14_821_0
ER  - 
%0 Journal Article
%A Salim Bouzebda
%A Issam Elhattab
%T A strong consistency of a nonparametric estimate of entropy under random censorship
%J Comptes Rendus. Mathématique
%D 2009
%P 821-826
%V 347
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2009.04.021
%G en
%F CRMATH_2009__347_13-14_821_0
Salim Bouzebda; Issam Elhattab. A strong consistency of a nonparametric estimate of entropy under random censorship. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 821-826. doi : 10.1016/j.crma.2009.04.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.021/

[1] J. Beirlant; E.J. Dudewicz; L. Györfi; E.C. van der Meulen Nonparametric entropy estimation: an overview, Int. J. Math. Stat. Sci., Volume 6 (1997) no. 1, pp. 17-39

[2] A. Carbonez; L. Györfi; E.C. van der Meulen Nonparametric entropy estimation based on randomly censored data, Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., Volume 20 (1991) no. 6, pp. 441-451

[3] P. Deheuvels; J.H.J. Einmahl On the strong limiting behavior of local functionals of empirical processes based upon censored data, Ann. Probab., Volume 24 (1996) no. 1, pp. 504-525

[4] P. Deheuvels; J.H.J. Einmahl Functional limit laws for the increments of Kaplan–Meier product-limit processes and applications, Ann. Probab., Volume 28 (2000) no. 3, pp. 1301-1335

[5] S. Diehl; W. Stute Kernel density and hazard function estimation in the presence of censoring, J. Multivariate Anal., Volume 25 (1988) no. 2, pp. 299-310

[6] A. Földes; L. Rejtő A LIL type result for the product limit estimator, Z. Wahrsch. Verw. Gebiete, Volume 56 (1981) no. 1, pp. 75-86

[7] A. Földes; L. Rejtő; B.B. Winter Strong consistency properties of nonparametric estimators for randomly censored data. The product-limit estimator, estimation of density and failure rate, Transactions of the Eighth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Prague, 1978), vol. C, Reidel, Dordrecht, 1979, pp. 105-121

[8] A. Földes; L. Rejtő; B.B. Winter Strong consistency properties of nonparametric estimators for randomly censored data. II. Estimation of density and failure rate, Period. Math. Hungar., Volume 12 (1981) no. 1, pp. 15-29

[9] E. Giné; D.M. Mason Uniform in bandwidth estimation of integral functionals of the density function, Scand. J. Statist., Volume 35 (2008) no. 4, pp. 739-761

[10] E.L. Kaplan; P. Meier Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc., Volume 53 (1958), pp. 457-481

[11] M.A. Tanner; W.H. Wong The estimation of the hazard function from randomly censored data by the kernel method, Ann. Statist., Volume 11 (1983) no. 3, pp. 989-993

[12] V. Viallon, Processus empiriques, estimation non paramétrique et données censurées, Ph.D. thesis, Université Paris 6, 2006

[13] G.S. Watson; M.R. Leadbetter Hazard analysis. I, Biometrika, Volume 51 (1964), pp. 175-184

[14] G.S. Watson; M.R. Leadbetter Hazard analysis. II, Sankhyā Ser. A, Volume 26 (1964), pp. 101-116

[15] B.B. Winter Nonparametric estimation with censored data from a distribution with nonincreasing density, Comm. Statist. Theory Methods, Volume 16 (1987) no. 1, pp. 93-120

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Uniform in bandwidth consistency of the kernel-type estimator of the Shannon's entropy

Salim Bouzebda; Issam Elhattab

C. R. Math (2010)

Loi du logarithme uniforme pour un estimateur non paramétrique de la régression en données censurées

Vivian Viallon

C. R. Math (2008)

Mean square convergence for estimators of additive regression under random censorship

Mohammed Debbarh; Vivian Viallon

C. R. Math (2007)