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.
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).
Accepted:
Published online:
@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, Volume 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] Empirical quantile process under type-2 progressive censoring, Statist. Probab. Lett., Volume 68 (2004), pp. 111-123
[2] Progressive Censoring, Birkhäuser, 2004
[3] Non-parametric estimation under progressive censoring, J. Statist. Plann. Inference, Volume 119 (2004), pp. 171-189
[4] Weighted Approximations in Probability and Statistics, John Wiley and Sons, England, 1993
[5] Strong Approximations in Probability and Statistics, Academic Press, New York, 1981
[6] 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] Strong invariance principles for arrays, Bull. Inst. Math. Acad. Sinica, Volume 28 (2000), pp. 167-181
[8] The law of the iterated logarithm for weighted sums of independent random variables, J. Theoret. Probab., Volume 16 (2003), pp. 519-542
Cited by Sources: