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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.

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1195-1213
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    References listed on IDEAS

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    1. 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.
    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, December.
    3. 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, June.
    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. 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.
    6. 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.
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    Cited by:

    1. Pablo Mart�nez-Camblor, 2011. "Testing the equality among distribution functions from independent and right censored samples via Cram�r--von Mises criterion," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1117-1131, March.
    2. Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
    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.
    4. N. Balakrishnan, 2007. "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 211-259, August.
    5. 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;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 325-341, August.

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