Statistics
On the quantile process under progressive censoring
[Sur le processus quantile sous censure progressive]
Comptes Rendus. Mathématique, Tome 347 (2009) no. 5-6, pp. 305-308.

Nous travaillons sur une représentation asymptotique presque-sûre du processus quantile sous censure progressive du type-II. Nous obtenons pour cette représentation une vitesse de convergence de type loi du logarithme itéré (LIL).

This work deals with an asymptotic almost-sure representation of the quantile process under type-II progressive censoring. A convergence rate of the law-of-the-iterated-logarithm type is obtained for this representation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.01.019
Alvarez-Andrade, Sergio 1

1 Laboratoire de mathématiques appliquées, Université de technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France
@article{CRMATH_2009__347_5-6_305_0,
     author = {Alvarez-Andrade, Sergio},
     title = {On the quantile process under progressive censoring},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {305--308},
     publisher = {Elsevier},
     volume = {347},
     number = {5-6},
     year = {2009},
     doi = {10.1016/j.crma.2009.01.019},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.019/}
}
TY  - JOUR
AU  - Alvarez-Andrade, Sergio
TI  - On the quantile process under progressive censoring
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 305
EP  - 308
VL  - 347
IS  - 5-6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2009.01.019/
DO  - 10.1016/j.crma.2009.01.019
LA  - en
ID  - CRMATH_2009__347_5-6_305_0
ER  - 
%0 Journal Article
%A Alvarez-Andrade, Sergio
%T On the quantile process under progressive censoring
%J Comptes Rendus. Mathématique
%D 2009
%P 305-308
%V 347
%N 5-6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2009.01.019/
%R 10.1016/j.crma.2009.01.019
%G en
%F CRMATH_2009__347_5-6_305_0
Alvarez-Andrade, Sergio. On the quantile process under progressive censoring. Comptes Rendus. Mathématique, Tome 347 (2009) no. 5-6, pp. 305-308. doi : 10.1016/j.crma.2009.01.019. http://www.numdam.org/articles/10.1016/j.crma.2009.01.019/

[1] Alvarez-Andrade, S.; Bordes, L. Empirical quantile process under type-2 progressive censoring, Statist. Probab. Lett., Volume 68 (2004), pp. 111-123

[2] Balakrishnan, N.; Aggarwala, R. Progressive Censoring, Birkhäuser, 2004

[3] Bordes, L. Non-parametric estimation under progressive censoring, J. Statist. Plann. Inference, Volume 119 (2004), pp. 171-189

[4] Csörgő, M.; Horváth, L. Weighted Approximations in Probability and Statistics, John Wiley and Sons, England, 1993

[5] Csörgő, M.; Révész, P. Strong Approximations in Probability and Statistics, Academic Press, New York, 1981

[6] Cuzick, J. A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab., Volume 8 (1995), pp. 625-641 (Erratum, “A strong law for weighted sums of i.i.d. random variables” J. Theoret. Probab., 14, 2001, pp. 605)

[7] Li, D.; Huang, M.L.; Rosalsky, A. Strong invariance principles for arrays, Bull. Inst. Math. Acad. Sinica, Volume 28 (2000), pp. 167-181

[8] Li, D.; Tomkins, R.J. The law of the iterated logarithm for weighted sums of independent random variables, J. Theoret. Probab., Volume 16 (2003), pp. 519-542

Cité par Sources :