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

Ta Cong Son (), Le Van Dung (), Bui Khanh Hang () and Tran Manh Cuong ()
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Ta Cong Son: VNU University of Science
Le Van Dung: The University of Da Nang - University of Science and Education
Bui Khanh Hang: VNU University of Science
Tran Manh Cuong: VNU University of Science

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-32

Abstract: Abstract 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.

Keywords: Marcinkiewicz laws of large numbers; Dependent random variables; Weighted sums; Heavy-tailed distributions; 60B12; 60F05; 60F15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10204-3

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