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Strong Convergence Properties for Weighted Sums of Extended Negatively Dependent Random Variables Under Sub-linear Expectations with Statistical Applications

Author

Listed:
  • Liangxue Li

    (Anhui University)

  • Xiaoqian Zheng

    (Anhui University)

  • Haiwu Huang

    (Guilin University of Aerospace Technology)

  • Xuejun Wang

    (Anhui University)

Abstract

In this paper, we establish the complete f-moment convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of extended negatively dependent (END, for short) random variables under sub-linear expectations, which extend and improve corresponding ones in sub-linear expectation space. As applications of the main results, the complete consistency and strong consistency of weighted estimators in nonparametric regression models under sub-linear expectations are also obtained.

Suggested Citation

  • Liangxue Li & Xiaoqian Zheng & Haiwu Huang & Xuejun Wang, 2024. "Strong Convergence Properties for Weighted Sums of Extended Negatively Dependent Random Variables Under Sub-linear Expectations with Statistical Applications," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-36, September.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10092-z
    DOI: 10.1007/s11009-024-10092-z
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    References listed on IDEAS

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    1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    2. Aiting Shen, 2016. "Complete convergence for weighted sums of END random variables and its application to nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 702-715, October.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
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