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Moment inequalities for m-negatively associated random variables and their applications

Author

Listed:
  • Aiting Shen

    (Anhui University)

  • Yu Zhang

    (Anhui University)

  • Benqiong Xiao

    (Anhui University)

  • Andrei Volodin

    (University of Regina)

Abstract

The moment inequalities for m-NA random variables, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality are established and the Khintchine–Kolmogorov convergence theorem and the three series theorem for m-NA random variables are also obtained. As one application of the moment inequalities, we study the large deviation for least squares estimator in nonlinear regression models under some general conditions. As another application, we investigate the strong consistency for least squares estimator in multiple linear regression models based on m-NA random variables.

Suggested Citation

  • Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0731-x
    DOI: 10.1007/s00362-015-0731-x
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    References listed on IDEAS

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    1. Gui-Jing, Chen & Lai, T. L. & Wei, C. Z., 1981. "Convergence systems and strong consistency of least squares estimates in regression models," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 319-333, September.
    2. H. Zarei & H. Jabbari, 2011. "Complete convergence of weighted sums under negative dependence," Statistical Papers, Springer, vol. 52(2), pages 413-418, May.
    3. Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 135-144.
    4. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.
    5. Prakasa Rao, B. L. S., 1984. "The rate of convergence of the least squares estimator in a non-linear regression model with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 14(3), pages 315-322, June.
    6. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
    7. Ling, Nengxiang, 2008. "The Bahadur representation for sample quantiles under negatively associated sequence," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2660-2663, November.
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    Cited by:

    1. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.

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