Strong consistency of tail value-at-risk estimator and corresponding general results under widely orthant dependent samples

Jinyu Zhou, Jigao Yan () and Dongya Cheng
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Jinyu Zhou: Soochow University
Jigao Yan: Soochow University
Dongya Cheng: Soochow University

Statistical Papers, 2024, vol. 65, issue 6, No 2, 3357-3394

Abstract: Abstract In this paper, strong consistency of tail value-at-risk (TVaR) estimator under widely orthant dependent (WOD) samples is established, and a numerical simulation is performed to verify the validity of the theoretical results. To reveal the essence of the result, theoretical discussion on complete and complete moment convergence corresponding to the Baum–Katz law, as well as the Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for maximal weighted sums and maximal product sums of widely orthant dependent (WOD) random variables are investigated. The results obtained in the context extend the corresponding ones for independent and some dependent random variables.

Keywords: Strong consistency; Tail value-at-risk; Widely orthant dependent random variables; Product sums; Complete convergence; Complete moment convergence; 60F15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01525-x

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