Comptes Rendus
no. 5-6
Statistics
On the quantile process under progressive censoring
[Sur le processus quantile sous censure progressive]

Présenté par : Paul Malliavin

Sergio Alvarez-Andrade1
1 Laboratoire de mathématiques appliquées, Université de technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France
Comptes Rendus. Mathématique, Volume 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
Sergio Alvarez-Andrade 1

1 Laboratoire de mathématiques appliquées, Université de technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France 
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Sergio Alvarez-Andrade. On the quantile process under progressive censoring. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 305-308. doi : 10.1016/j.crma.2009.01.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.01.019/

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

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

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

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

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

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

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