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June 2022 A heteroscedasticity diagnostic of a regression analysis with copula dependent random variables
Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar
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Braz. J. Probab. Stat. 36(2): 408-419 (June 2022). DOI: 10.1214/22-BJPS532


One of the most important assumptions in multiple regression analysis is the independence of the explanatory variables, however, this assumption is violated in several situations. In this work, we investigate regression equations when this independence does not hold and the explanatory variables are connected by many of elliptical copulas. We apply the proposed regression equation to study its heteroscedasticity diagnostic and using simulated data we also assess our regression model. A cross-validation procedure is carried out to ensure the unbiasedness of the results. Also, a real data analysis is presented as an application.

Funding Statement

The work of the third author was supported by the project APVV-18-0052 and VEGA 1/0006/19.


The authors wish to thank the anonymous reviewers for the comments and suggestions that did lead to a significant improvement of the original manuscript.


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Ayyub Sheikhi. Fereshteh Arad. Radko Mesiar. "A heteroscedasticity diagnostic of a regression analysis with copula dependent random variables." Braz. J. Probab. Stat. 36 (2) 408 - 419, June 2022.


Received: 1 February 2021; Accepted: 1 February 2022; Published: June 2022
First available in Project Euclid: 5 May 2022

Digital Object Identifier: 10.1214/22-BJPS532

Keywords: Gaussian copula , Heteroscedasticity , regression , t-copula

Rights: This research was funded, in whole or in part, by [Slovak Research and Development Agency; Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic, APVV-18-0052 and VEGA 1/0006/19]. A CC BY 4.0 license is applied to this article arising from this submission, in accordance with the grant’s open access conditions


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Vol.36 • No. 2 • June 2022
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