IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v168y2018icp304-322.html
   My bibliography  Save this article

Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics

Author

Listed:
  • Jin, Ze
  • Matteson, David S.

Abstract

We propose three new measures of mutual dependence between multiple random vectors. Each measure is zero if and only if the random vectors are mutually independent. The first generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance covariances. The proposed measures share similar properties and asymptotic distributions with distance covariance, and capture non-linear and non-monotone mutual dependence between the random vectors. Inspired by complete and incomplete V-statistics, we define empirical and simplified empirical measures as a trade-off between the complexity and statistical power when testing mutual independence. The implementation of corresponding tests is demonstrated by both simulation results and real data examples.

Suggested Citation

  • Jin, Ze & Matteson, David S., 2018. "Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 304-322.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:304-322
    DOI: 10.1016/j.jmva.2018.08.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17307832
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2018.08.006?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. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    2. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    3. David S. Matteson & Ruey S. Tsay, 2017. "Independent Component Analysis via Distance Covariance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 623-637, April.
    4. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    5. Xiaofeng Shao & Jingsi Zhang, 2014. "Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1302-1318, September.
    6. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    7. Bilodeau, M. & Lafaye de Micheaux, P., 2005. "A multivariate empirical characteristic function test of independence with normal marginals," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 345-369, August.
    8. Fang Han & Shizhe Chen & Han Liu, 2017. "Distribution-free tests of independence in high dimensions," Biometrika, Biometrika Trust, vol. 104(4), pages 813-828.
    9. Fan, Yanan & de Micheaux, Pierre Lafaye & Penev, Spiridon & Salopek, Donna, 2017. "Multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 189-210.
    10. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    11. Shun Yao & Xianyang Zhang & Xiaofeng Shao, 2018. "Testing mutual independence in high dimension via distance covariance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 455-480, June.
    12. Kojadinovic, Ivan & Holmes, Mark, 2009. "Tests of independence among continuous random vectors based on Cramr-von Mises functionals of the empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1137-1154, July.
    13. Szekely, Gábor J. & Rizzo, Maria L., 2005. "A new test for multivariate normality," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 58-80, March.
    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. Christian Gourieroux & Joann Jasiak, 2023. "Generalized Covariance Estimator," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1315-1327, October.
    2. Beaulieu Guillaume Boglioni & de Micheaux Pierre Lafaye & Ouimet Frédéric, 2021. "Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin," Dependence Modeling, De Gruyter, vol. 9(1), pages 424-438, January.
    3. Krzyśko Mirosław & Smaga Łukasz, 2020. "Measuring and Testing Mutual Dependence of Multivariate Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 21-37, September.
    4. Mirosław Krzyśko & Łukasz Smaga, 2020. "Measuring and Testing Mutual Dependence of Multivariate Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 21-37, September.

    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. Ivair R. Silva & Yan Zhuang & Julio C. A. da Silva Junior, 2022. "Kronecker delta method for testing independence between two vectors in high-dimension," Statistical Papers, Springer, vol. 63(2), pages 343-365, April.
    2. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    3. Yongshuai Chen & Wenwen Guo & Hengjian Cui, 2024. "On the test of covariance between two high-dimensional random vectors," Statistical Papers, Springer, vol. 65(5), pages 2687-2717, July.
    4. Kalemkerian, Juan & Fernández, Diego, 2020. "An independence test based on recurrence rates," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    5. Fan, Yanan & de Micheaux, Pierre Lafaye & Penev, Spiridon & Salopek, Donna, 2017. "Multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 189-210.
    6. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    7. Dehghan, Sakineh & Faridrohani, Mohammad Reza, 2024. "A data depth based nonparametric test of independence between two random vectors," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    8. Shi, Huai-Long & Zhou, Wei-Xing, 2022. "Factor volatility spillover and its implications on factor premia," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    9. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    10. Cakici, Nusret & Zaremba, Adam, 2022. "Salience theory and the cross-section of stock returns: International and further evidence," Journal of Financial Economics, Elsevier, vol. 146(2), pages 689-725.
    11. Chue, Timothy K. & Gul, Ferdinand A. & Mian, G. Mujtaba, 2019. "Aggregate investor sentiment and stock return synchronicity," Journal of Banking & Finance, Elsevier, vol. 108(C).
    12. Monica Martinez-Blasco & Vanessa Serrano & Francesc Prior & Jordi Cuadros, 2023. "Analysis of an event study using the Fama–French five-factor model: teaching approaches including spreadsheets and the R programming language," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-34, December.
    13. Po-Hsuan Hsu & Dongmei Li & Qin Li & Siew Hong Teoh & Kevin Tseng, 2022. "Valuation of New Trademarks," Management Science, INFORMS, vol. 68(1), pages 257-279, January.
    14. Ciciretti, Rocco & Dalò, Ambrogio & Dam, Lammertjan, 2023. "The contributions of betas versus characteristics to the ESG premium," Journal of Empirical Finance, Elsevier, vol. 71(C), pages 104-124.
    15. Jeong, Giho & Kang, Jangkoo & Kwon, Kyung Yoon, 2018. "Liquidity skewness premium," The North American Journal of Economics and Finance, Elsevier, vol. 46(C), pages 130-150.
    16. Liu, Siqi & Yin, Chao & Zeng, Yeqin, 2021. "Abnormal investment and firm performance," International Review of Financial Analysis, Elsevier, vol. 78(C).
    17. Yu Wang & Haicheng Shu, 2019. "Evaluating the Performance of Factor Pricing Models for Different Stock Market Trends: Evidence from China," Working Papers 2019-10-10, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    18. François-Éric Racicot & Raymond Théoret, 2022. "Tracking market and non-traditional sources of risks in procyclical and countercyclical hedge fund strategies under extreme scenarios: a nonlinear VAR approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-56, December.
    19. Berggrun, Luis & Cardona, Emilio & Lizarzaburu, Edmundo, 2020. "Firm profitability and expected stock returns: Evidence from Latin America," Research in International Business and Finance, Elsevier, vol. 51(C).
    20. Grobys, Klaus & Haga, Jesper, 2016. "Identifying portfolio-based systematic risk factors in equity markets," Finance Research Letters, Elsevier, vol. 17(C), pages 88-92.

    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:jmvana:v:168:y:2018:i:c:p:304-322. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.