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Exact Non‐parametric Confidence Intervals for Quantiles with Progressive Type‐II Censoring

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  • Olivier Guilbaud

Abstract

It is shown how various exact non‐parametric inferences based on order statistics in one or two random samples can be generalized to situations with progressive type‐II censoring, which is a kind of evolutionary right censoring. Ordinary type‐II right censoring is a special case of such progressive censoring. These inferences include confidence intervals for a given parent quantile, prediction intervals for a given order statistic of a future sample, and related two‐sample inferences based on exceedance probabilities. The proposed inferences are valid for any parent distribution with continuous distribution function. The key result is that each observable uncensored order statistic that becomes available with progressive type‐II censoring can be represented as a mixture with known weights of underlying ordinary order statistics. The importance of this mixture representation lies in that various properties of such observable order statistics can be deduced immediately from well‐known properties of ordinary order statistics.

Suggested Citation

  • 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, December.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:4:p:699-713
    DOI: 10.1111/1467-9469.00263
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    Cited by:

    1. Fischer, T. & Balakrishnan, N. & Cramer, E., 2008. "Mixture representation for order statistics from INID progressive censoring and its applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1999-2015, October.
    2. 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.
    3. 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.
    4. Alvarez-Andrade, Sergio & Bordes, Laurent, 2004. "Empirical quantile process under type-II progressive censoring," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 111-123, June.
    5. Ahmadi, J. & Balakrishnan, N., 2005. "Distribution-free confidence intervals for quantile intervals based on current records," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 190-202, December.
    6. Beutner, E. & Cramer, E., 2014. "Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 95-109.

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