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AIMS Mathematics

2022, Volume 7, Issue 8: 13704-13732. doi: 10.3934/math.2022755
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Research article

Bootstrapping $ m $-generalized order statistics with variable rank

  • 1.
    Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
  • 2.
    Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt
  • 3.
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
  • Received: 21 January 2022 Revised: 11 April 2022 Accepted: 23 April 2022 Published: 23 May 2022

  • MSC : 62F20, 62F40, 62G30

  • In this paper, several bootstrap properties of $ m $-generalized order statistics ($ m $-GOSs) with variable rank (central and intermediate) are revealed. We study the inconsistency, weak consistency and strong consistency of bootstrapping central and intermediate $ m $-GOSs when the normalizing constants are assumed to be known or estimated from the re-sampled data using a proper re-sample size. Furthermore, sufficient conditions for the weak and strong consistencies of the bootstrapping distributions of central and intermediate $ m $-GOSs based on the normalizing constant estimators are given. Finally, a simulation study is conducted to determine the optimal bootstrap re-sample size corresponding to the best fitting of the bootstrapping distribution.

    Citation: H. M. Barakat, Magdy E. El-Adll, M. E. Sobh. Bootstrapping $ m $-generalized order statistics with variable rank[J]. AIMS Mathematics, 2022, 7(8): 13704-13732. doi: 10.3934/math.2022755

    Related Papers:

  • In this paper, several bootstrap properties of $ m $-generalized order statistics ($ m $-GOSs) with variable rank (central and intermediate) are revealed. We study the inconsistency, weak consistency and strong consistency of bootstrapping central and intermediate $ m $-GOSs when the normalizing constants are assumed to be known or estimated from the re-sampled data using a proper re-sample size. Furthermore, sufficient conditions for the weak and strong consistencies of the bootstrapping distributions of central and intermediate $ m $-GOSs based on the normalizing constant estimators are given. Finally, a simulation study is conducted to determine the optimal bootstrap re-sample size corresponding to the best fitting of the bootstrapping distribution.


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