IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp55-67.html
   My bibliography  Save this article

Validation of association

Author

Listed:
  • Ćmiel, Bogdan
  • Ledwina, Teresa

Abstract

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests for independence and to provide an easily interpretable diagnostic plot of existing departures from the null model. The dependence function is designed to detect general dependence structure between variables in quantiles of the joint distribution. It gives an insight into how the dependence structure changes in different parts of the joint distribution. We define new estimators of the dependence function, discuss some of their properties, and apply them to construct new tests of independence. Numerical evidence is given to the tests benefits against three recognized independence tests introduced in the previous years. In real-data analysis, we offer the use of our tests and the graphical presentation of the underlying dependence structure.

Suggested Citation

  • Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:55-67
    DOI: 10.1016/j.insmatheco.2019.12.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016766871930424X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2019.12.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R'emy Chicheportiche, 2013. "Non-linear dependences in finance," Papers 1309.5073, arXiv.org.
    2. Dhaene, Jan & Denuit, Michel & Vanduffel, Steven, 2009. "Correlation order, merging and diversification," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 325-332, December.
    3. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    4. Nuo Xu & Xuan Huang & Samuel Huang, 2017. "A measure of general functional dependence between two continuous variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(9), pages 4327-4352, May.
    5. Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.
    6. Teresa Ledwina & Grzegorz Wyłupek, 2012. "Two-Sample Test Against One-Sided Alternatives," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 358-381, June.
    7. Genest C. & Boies J-C., 2003. "Detecting Dependence With Kendall Plots," The American Statistician, American Statistical Association, vol. 57, pages 275-284, November.
    8. Shurong Zheng & Ning-Zhong Shi & Zhengjun Zhang, 2012. "Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1239-1252, September.
    9. Deheuvels, Paul & Peccati, Giovanni & Yor, Marc, 2006. "On quadratic functionals of the Brownian sheet and related processes," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 493-538, March.
    10. Linton, O. & Whang, Yoon-Jae, 2007. "The quantilogram: With an application to evaluating directional predictability," Journal of Econometrics, Elsevier, vol. 141(1), pages 250-282, November.
    11. Kaas, R., 1993. "How to (and how not to) compute stop-loss premiums in practice," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 241-254, December.
    12. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," LIDAM Reprints ISBA 2017005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Albert Vexler & Wan-Min Tsai & Alan D. Hutson, 2014. "A Simple Density-Based Empirical Likelihood Ratio Test for Independence," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 158-169, February.
    15. Albers, Willem, 1999. "Stop-loss premiums under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 173-185, May.
    16. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 266-281.
    17. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 35-51.
    18. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 62-82, March.
    19. X. Wang & B. Jiang & J. S. Liu, 2017. "Generalized R-squared for detecting dependence," Biometrika, Biometrika Trust, vol. 104(1), pages 129-139.
    20. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    21. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
    22. Ruth Heller & Yair Heller & Malka Gorfine, 2013. "A consistent multivariate test of association based on ranks of distances," Biometrika, Biometrika Trust, vol. 100(2), pages 503-510.
    23. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," LIDAM Reprints ISBA 2018018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    24. Bagkavos, D. & Patil, P.N., 2017. "A new test of independence for bivariate observations," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 117-133.
    25. Dhaene, J. & Goovaerts, M. J., 1997. "On the dependency of risks in the individual life model," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 243-253, May.
    26. Friedrich Schmid & Rafael Schmidt, 2007. "Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 323-354, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kojadinovic, Ivan & Stemikovskaya, Kristina, 2019. "Subsampling (weighted smooth) empirical copula processes," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 704-723.
    2. Berghaus, Betina & Segers, Johan, 2017. "Weak convergence of the weighted empirical beta copula process," LIDAM Discussion Papers ISBA 2017015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.
    4. Berghaus, Betina & Segers, Johan, 2018. "Weak convergence of the weighted empirical beta copula process," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 266-281.
    5. Reijnen, Rajko & Albers, Willem & Kallenberg, Wilbert C.M., 2005. "Approximations for stop-loss reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 237-250, June.
    6. Davis, Richard & Drees, Holger & Segers, Johan & Warchol, Michal, 2018. "Inference on the tail process with application to financial time series modelling," LIDAM Discussion Papers ISBA 2018002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Kiriliouk, Anna & Segers, Johan & Tsukahara, Hideatsu, 2019. "On Some Resampling Procedures with the Empirical Beta Copula," LIDAM Discussion Papers ISBA 2019012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    9. Junker, Robert R. & Griessenberger, Florian & Trutschnig, Wolfgang, 2021. "Estimating scale-invariant directed dependence of bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    10. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Papers 2011.00909, arXiv.org, revised Mar 2021.
    11. Dietmar Pfeifer & Olena Ragulina, 2020. "Adaptive Bernstein Copulas and Risk Management," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    12. Hofert, Marius & Prasad, Avinash & Zhu, Mu, 2022. "Multivariate time-series modeling with generative neural networks," Econometrics and Statistics, Elsevier, vol. 23(C), pages 147-164.
    13. Ledwina, Teresa & Wyłupek, Grzegorz, 2014. "Validation of positive quadrant dependence," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 38-47.
    14. Kiriliouk, Anna & Segers, Johan & Tafakori, Laleh, 2018. "An estimator of the stable tail dependence function based on the empirical beta copula," LIDAM Discussion Papers ISBA 2018029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    16. Tobias Fissler & Marc-Oliver Pohle, 2023. "Generalised Covariances and Correlations," Papers 2307.03594, arXiv.org, revised Sep 2023.
    17. Lu Lu & Sujit Ghosh, 2023. "Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods," Mathematics, MDPI, vol. 11(20), pages 1-22, October.
    18. Kiriliouk, Anna & Segers, Johan & Tafakori, Laleh, 2017. "An estimator of the stable tail dependence function based on the empirical beta copula," LIDAM Discussion Papers ISBA 2017028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Jozef Baruník & Tobias Kley, 2019. "Quantile coherency: A general measure for dependence between cyclical economic variables," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 131-152.
    20. Valdivia Coria, Joab Dan, 2022. "Apalancamiento, ciclo financiero y económico [Leverage, financial and business cycles]," MPRA Paper 116849, University Library of Munich, Germany.

    More about this item

    Keywords

    Copula; Cross-quantilogram; Independence testing; Measure of dependence; Quantile dependence function; Weighted statistics;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:55-67. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.