Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables

Yuta Tanoue

doi:10.3934/puqr.2021003

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2021, Volume 6, Issue 1: 53-60. Doi: 10.3934/puqr.2021003

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Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables

Yuta Tanoue^,

Institute for Business and Finance, Waseda University, 3rd Floor, Bldg.11 1-6-1 Nishi-Waseda, Shinjuku-ku, 169-8050 Tokyo, JP Full list of author information is available at the end of the article

Email: tanoue.yuta@aoni.waseda.jp
Email: tanoue.yuta@aoni.waseda.jp

Received: January 29, 2020

Accepted: January 05, 2021

Published: March 2021

This work was supported by JSPS Grant-in-Aid for Young Scientists(Grant No.18K12873) and Waseda University Grants for Special Research Projects(“Tokutei Kadai”) (Grant No. 2019C-688). The authour thanks the anonymous referee and the associate editor for their careful reading of the paper and constructive comments.

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Abstract

When addressing various financial problems, such as estimating stock portfolio risk, it is necessary to derive the distribution of the sum of the dependent random variables. Although deriving this distribution requires identifying the joint distribution of these random variables, exact estimation of the joint distribution of dependent random variables is difficult. Therefore, in recent years, studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty. In this study, we obtain an improved Hoeffding inequality for dependent bounded variables. Further, we expand the above result to the case of sub-Gaussian random variables.

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Mathematics Subject Classification: 60F10; 37A25.

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