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Empirical quantile process under type-II progressive censoring

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  • Alvarez-Andrade, Sergio
  • Bordes, Laurent
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    Abstract

    This work deals with asymptotic properties of the [[alpha]m]th-order statistic of a type-II progressively censored sample of size m. Such an order statistic, indexed by [alpha][set membership, variant][0,1], is called the quantile process. Our main results concern the normalized version of the quantile process for which a weak convergence result is obtained. This result is applied in order to construct non-parametric estimators of quantiles. Monte-Carlo simulations illustrate the behavior of the estimators for limited sample size.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00075-6
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 1 (June)
    Pages: 111-123

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:1:p:111-123
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    Keywords: Weak convergence Martingales Monte-Carlo study Progressive censoring Quantile process Reliability Variance estimators;

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    1. Olivier Guilbaud, 2001. "Exact Non-parametric Confidence Intervals for Quantiles with Progressive Type-II Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 699-713.
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    Cited by:

    1. Sergio Alvarez-Andrade & N. Balakrishnan & Laurent Bordes, 2009. "Proportional hazards regression under progressive Type-II censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 887-903, December.
    2. N. Balakrishnan & E. Beutner & E. Cramer, 2010. "Exact two-sample nonparametric confidence, prediction, and tolerance intervals based on ordinary and progressively type-II right censored data," TEST- An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 68-91, May.
    3. Udo Kamps & Erhard Cramer, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST- An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 271-275, August.
    4. Ayman M. Abd-Elrahman & Khalaf S. Sultan, 2007. "Reliability estimation based on general progressive censored data from theWeibull model: comparison between Bayesian and classical approaches," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 239-257.
    5. Alvarez-Andrade, S. & Balakrishnan, N. & Bordes, L., 2007. "Homogeneity tests based on several progressively Type-II censored samples," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1195-1213, July.

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