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<p>In this paper, based on the theory of regularly varying functions we investigate the general Marcinkiewicz laws of large numbers for weighted sums of negatively associated random variables with heavy-tail. As applications of our main results, we study the consistency for conditional Value-at-Risk estimator with heavy-tailed samples as well as the consistency for the weighted estimator in a semiparametric regression model based on heavy-tailed errors.</p>

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The Marcinkiewicz Laws for Weighted Sums of Heavy-Tailed Random Variables and Applications to the Value-at-Risk Estimators and Semiparametric Regression Models

  • 期刊论文

  • 发表日期：

    2025年9月17日

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  • Ta Cong Son,
  • Le Van Dung,
  • Bui Khanh Hang,
  • Tran Manh Cuong

摘要

In this paper, based on the theory of regularly varying functions we investigate the general Marcinkiewicz laws of large numbers for weighted sums of negatively associated random variables with heavy-tail. As applications of our main results, we study the consistency for conditional Value-at-Risk estimator with heavy-tailed samples as well as the consistency for the weighted estimator in a semiparametric regression model based on heavy-tailed errors.