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A necessary test for complete independence in high dimensions using rank-correlations

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  • Wang, Guanghui
  • Zou, Changliang
  • Wang, Zhaojun

Abstract

We propose a nonparametric necessary test for the complete independence of random variables in high-dimensional environment. The test is constructed based on Spearman’s rank-correlations and is shown to be asymptotically normal by the martingale central limit theorem as both the sample size and the dimension of variables go to infinity. Simulation studies show that the proposed test works well in finite-sample situations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:121:y:2013:i:c:p:224-232
    DOI: 10.1016/j.jmva.2013.05.014
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    References listed on IDEAS

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    1. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
    2. Jiajuan Liang & Kai-Tai Fang & Fred Hickernell, 2008. "Some necessary uniform tests for spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 679-696, September.
    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. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    5. Fan, Jianqing & Peng, Heng & Huang, Tao, 2005. "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 781-796, September.
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    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. 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.

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