IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v117y2018icp128-137.html
   My bibliography  Save this article

Testing independence in high dimensions using Kendall’s tau

Author

Listed:
  • Mao, Guangyu

Abstract

To check the total independence of a random vector without Gaussian assumption in high dimensions, Leung and Drton (forthcoming) recently developed a test by virtue of pairwise Kendall’s taus. However, as their simulation shows, the test suffers from noticeable size distortion when the sample size is small. The present paper provides a theoretical explanation about this phenomenon, and accordingly proposes a new test. The new test can be justified when both the dimension and the sample size go to infinity simultaneously, and moreover, it can be even justified when the dimension tends to infinity but the sample size is fixed, which implies that the test can perform well in the cases of small sample size. Simulation studies confirm the theoretical findings, and show that the newly proposed test can bring remarkable improvement. To illustrate the use of the new test, a real data set is also analyzed.

Suggested Citation

  • Mao, Guangyu, 2018. "Testing independence in high dimensions using Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 128-137.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:128-137
    DOI: 10.1016/j.csda.2017.07.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317301743
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.07.012?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. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    2. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
    3. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
    4. Mao, Guangyu, 2014. "A new test of independence for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 14-18.
    5. Guangyu Mao, 2017. "Robust test for independence in high dimensions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10036-10050, October.
    6. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    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. He, Daojiang & Liu, Huanyu & Xu, Kai & Cao, Mingxiang, 2021. "Generalized Schott type tests for complete independence in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Jone Ascorbebeitia & Eva Ferreira & Susan Orbe, 2022. "Testing conditional multivariate rank correlations: the effect of institutional quality on factors influencing competitiveness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 931-949, December.
    3. Long Feng & Yanling Ding & Binghui Liu, 2020. "Rank‐based Tests for Cross‐sectional Dependence in Large (N, T) Fixed Effects Panel Data Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(5), pages 1198-1216, October.
    4. Yuangang Li & Maohua Sun & Guanghui Yuan & Yujing Liu, 2019. "Evaluation Methods of Water Environment Safety and Their Application to the Three Northeast Provinces of China," Sustainability, MDPI, vol. 11(18), pages 1-16, September.
    5. 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.
    6. Deng, Wenli & Wang, Jinglong & Zhang, Riquan, 2022. "Measures of concordance and testing of independence in multivariate structure," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    7. Feng, Long & Zhao, Ping & Ding, Yanling & Liu, Binghui, 2021. "Rank-based tests of cross-sectional dependence in panel data models," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

    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. Mao, Guangyu, 2015. "A note on testing complete independence for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 82-85.
    2. He, Daojiang & Liu, Huanyu & Xu, Kai & Cao, Mingxiang, 2021. "Generalized Schott type tests for complete independence in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Masashi Hyodo & Nobumichi Shutoh & Takahiro Nishiyama & Tatjana Pavlenko, 2015. "Testing block-diagonal covariance structure for high-dimensional data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 460-482, November.
    4. Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2013. "A necessary test for complete independence in high dimensions using rank-correlations," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 224-232.
    5. Long Feng & Changliang Zou & Zhaojun Wang, 2016. "Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 721-735, April.
    6. Yamada, Yuki & Hyodo, Masashi & Nishiyama, Takahiro, 2017. "Testing block-diagonal covariance structure for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 305-316.
    7. Aki Ishii & Kazuyoshi Yata & Makoto Aoshima, 2021. "Hypothesis tests for high-dimensional covariance structures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 599-622, June.
    8. Bierens, H.J. & Broersma, L., 1991. "The relation between unemployment and interest rate : some international evidence," Serie Research Memoranda 0112, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    9. Juncal Cunado & David Gabauer & Rangan Gupta, 2024. "Realized volatility spillovers between energy and metal markets: a time-varying connectedness approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-17, December.
    10. Elie Bouri & Georges Azzi, 2014. "On the Dynamic Transmission of Mean and Volatility across the Arab Stock Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 13(3), pages 279-304, December.
    11. Eric Fur, 2023. "Risk and return of classic car market prices: passion or financial investment?," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 59-68, February.
    12. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    13. Ericsson, Neil R., 2016. "Eliciting GDP forecasts from the FOMC’s minutes around the financial crisis," International Journal of Forecasting, Elsevier, vol. 32(2), pages 571-583.
    14. Jin, Xiaoye, 2015. "Volatility transmission and volatility impulse response functions among the Greater China stock markets," Journal of Asian Economics, Elsevier, vol. 39(C), pages 43-58.
    15. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    16. Damian Jelito & Marcin Pitera, 2018. "New fat-tail normality test based on conditional second moments with applications to finance," Papers 1811.05464, arXiv.org, revised Apr 2020.
    17. Ilham Haouas & Naceur Kheraief & Arusha Cooray & Syed Jawad Hussain Shahzad, 2019. "Time-Varying Casual Nexuses Between Remittances and Financial Development in Some MENA Countries," Working Papers 1294, Economic Research Forum, revised 2019.
    18. Lenten, Liam J.A. & Geerling, Wayne & Kónya, László, 2012. "A hedonic model of player wage determination from the Indian Premier League auction: Further evidence," Sport Management Review, Elsevier, vol. 15(1), pages 60-71.
    19. Stephen Keef & Melvin Roush, 2005. "Day-of-the-week effects in the pre-holiday returns of the Standard & Poor's 500 stock index," Applied Financial Economics, Taylor & Francis Journals, vol. 15(2), pages 107-119.
    20. Martha Misas A. & Carlos Esteban Posada P & Diego Mauricio Vásquez E, 2003. "¿Está determinado el nivel de precios por las expectativas de dinero y producto en Colombia?," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República, vol. 21(43), pages 8-31, June.

    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:csdana:v:117:y:2018:i:c:p:128-137. 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/csda .

    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.