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Homogeneity tests based on several progressively Type-II censored samples

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  • Alvarez-Andrade, S.
  • Balakrishnan, N.
  • Bordes, L.
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    Abstract

    In this paper, we discuss the problem of testing the homogeneity of several populations when the available data are progressively Type-II censored. Defining for each sample a univariate counting process, we can modify all the methods that were developed during the last two decades (see e.g. [P.K. Andersen, Ø. Borgan, R. Gill, N. Keiding, Statistical Models Based on Counting Processes, Springer, New York, 1993]) for use to this problem. An important aspect of these tests is that they are based on either linear or non-linear functionals of a discrepancy process (DP) based on the comparison of the cumulative hazard rate (chr) estimated from each sample with the chr estimated from the whole sample (viz., the aggregation of all the samples), leading to either linear tests or non-linear tests. Both these kinds of tests suffer from some serious drawbacks. For example, it is difficult to extend non-linear tests to the K-sample situation when K[greater-or-equal, slanted]3. For this reason, we propose here a new class of non-linear tests, based on a chi-square type functional of the DP, that can be applied to the K-sample problem for any K[greater-or-equal, slanted]2.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 6 (July)
    Pages: 1195-1213

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1195-1213

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    Related research

    Keywords: Progressive censoring Counting processes Homogeneity tests Chi-square tests Reliability;

    References

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    1. 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.
    2. 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.
    3. Kirmani, Syed N. U. A. & Dauxois, Jean-Yves, 2003. "Testing relative risk under random censoring," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 1-7, March.
    4. Basak, Indrani & Balakrishnan, N., 2003. "Robust estimation under progressive censoring," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 349-376, October.
    5. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    6. Olivier Guilbaud, 2004. "Exact Non-Parametric Confidence, Prediction and Tolerance Intervals with Progressive Type-II Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 31(2), pages 265-281.
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    Cited by:
    1. Gopaldeb Chattopadhyay & Indranil Mukhopadhyay, 2010. "Progressive censoring under inverse sampling for nonparametric multi-sample location problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(2), pages 325-341, August.
    2. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 211-259, August.
    3. 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.

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