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<p>In this paper, the authors investigate the double-indexed version of the strong law of large numbers under some general conditions in a sub-linear expectation space. The weighted version of the Marcinkiewicz-Zygmund type strong law of large numbers is also established. These results extend or improve some existing ones in the classical probability space or a sub-linear expectation space. As an application, they further study the nonparametric regression model under the sub-linear expectation framework. Some numerical simulations are also presented.</p>

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General Results on Strong Laws for Weighted Sums Under Sub-linear Expectations with a Statistical Application

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Yi Wu,
  • Mengmei Xi,
  • Xuejun Wang

摘要

In this paper, the authors investigate the double-indexed version of the strong law of large numbers under some general conditions in a sub-linear expectation space. The weighted version of the Marcinkiewicz-Zygmund type strong law of large numbers is also established. These results extend or improve some existing ones in the classical probability space or a sub-linear expectation space. As an application, they further study the nonparametric regression model under the sub-linear expectation framework. Some numerical simulations are also presented.