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On the rate of complete convergence for weighted sums of NSD random variables and an application

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Abstract

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.

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Acknowledgements

The authors are most grateful to the anonymous referees for the careful reading of the manuscript and valuable suggestions that helped significantly improving an earlier version of this paper.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Mohammad Amini & Abolghasem Bozorgnia

  2. Department of Statistics, Faculty of Mathematical Sciences, University of Sistan and Baluchestan, Zahedan, Iran

    Habib Naderi

  3. Department of Statistics, Khayyam University, Mashhad, Iran

    Abolghasem Bozorgnia

Authors
  1. Habib Naderi
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  2. Mohammad Amini
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  3. Abolghasem Bozorgnia
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Corresponding author

Correspondence to Mohammad Amini.

Additional information

This research was supported by a grant from Ferdowsi University of Mashhad (NO.2/42843).

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Naderi, H., Amini, M. & Bozorgnia, A. On the rate of complete convergence for weighted sums of NSD random variables and an application. Appl. Math. J. Chin. Univ. 32, 270–280 (2017). https://doi.org/10.1007/s11766-017-3437-0

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  • DOI: https://doi.org/10.1007/s11766-017-3437-0

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