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Quantile Association Regression Models

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  • Ruosha Li
  • Yu Cheng
  • Jason P. Fine

Abstract

It is often important to study the association between two continuous variables. In this work, we propose a novel regression framework for assessing conditional associations on quantiles. We develop general methodology which permits covariate effects on both the marginal quantile models for the two variables and their quantile associations. The proposed quantile copula models have straightforward interpretation, facilitating a comprehensive view of association structure which is much richer than that based on standard product moment and rank correlations. We show that the resulting estimators are uniformly consistent and weakly convergent as a process of the quantile index. Simple variance estimators are presented which perform well in numerical studies. Extensive simulations and a real data example demonstrate the practical utility of the methodology. Supplementary materials for this article are available online.

Suggested Citation

  • Ruosha Li & Yu Cheng & Jason P. Fine, 2014. "Quantile Association Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 230-242, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:230-242
    DOI: 10.1080/01621459.2013.847375
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    References listed on IDEAS

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    1. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    2. Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
    3. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.
    4. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
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    Cited by:

    1. Chi-Chuan Yang & Yi-Hau Chen & Hsing-Yi Chang, 2017. "Joint regression analysis of marginal quantile and quantile association: application to longitudinal body mass index in adolescents," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 1075-1090, November.
    2. Ruosha Li & Yu Cheng & Qingxia Chen & Jason Fine, 2017. "Quantile association for bivariate survival data," Biometrics, The International Biometric Society, vol. 73(2), pages 506-516, June.
    3. Guo, Ranran & Ye, Wuyi, 2021. "A model of dynamic tail dependence between crude oil prices and exchange rates," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    4. Ye, Wuyi & Luo, Kebing & Liu, Xiaoquan, 2017. "Time-varying quantile association regression model with applications to financial contagion and VaR," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1015-1028.
    5. Joanna Cichorska & Monika Klimontowicz, 2016. "Financialisation As A Result Of The Network Economy’S Development," "e-Finanse", University of Information Technology and Management, Institute of Financial Research and Analysis, vol. 12(2), pages 1-12, October.

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