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Testing for complete independence in high dimensions

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  • James R. Schott
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    Abstract

    A simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample size and, in particular, even when the number of variables exceeds the sample size. The finite sample size performance of the normal approximation is evaluated in a simulation study and the results are compared to those of the likelihood ratio test. Copyright 2005, Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/biomet/92.4.951
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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 92 (2005)
    Issue (Month): 4 (December)
    Pages: 951-956

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    Handle: RePEc:oup:biomet:v:92:y:2005:i:4:p:951-956

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    Cited by:
    1. Badi H. Baltagi & Chihwa Kao & Long Liu, 2013. "The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 241-270, September.
    2. Xiao, Han & Wu, Wei Biao, 2013. "Asymptotic theory for maximum deviations of sample covariance matrix estimates," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2899-2920.
    3. Qiu, Yumou & Chen, Songxi, 2012. "Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation," MPRA Paper 46242, University Library of Munich, Germany.
    4. Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
    5. Alexander Chudik & M. Hashem Pesaran, 2013. "Large Panel Data Models with Cross-Sectional Dependence: A Survey," CESifo Working Paper Series 4371, CESifo Group Munich.
    6. Mathias Drton & Han Xiao, 2010. "Finiteness of small factor analysis models," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(4), pages 775-783, August.
    7. Fujikoshi, Yasunori & Sakurai, Tetsuro & Yanagihara, Hirokazu, 2014. "Consistency of high-dimensional AIC-type and Cp-type criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 184-200.
    8. Mao, Guangyu, 2014. "A note on tests of sphericity and cross-sectional dependence for fixed effects panel model," Economics Letters, Elsevier, vol. 122(2), pages 215-219.
    9. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2012. "A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model," Journal of Econometrics, Elsevier, vol. 170(1), pages 164-177.
    10. Yukun Liu & Changliang Zou & Zhaojun Wang, 2013. "Calibration of the empirical likelihood for high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(3), pages 529-550, June.
    11. Fujikoshi, Yasunori & Sakurai, Tetsuro, 2009. "High-dimensional asymptotic expansions for the distributions of canonical correlations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 231-242, January.
    12. 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.
    13. Kato, Naohiro & Yamada, Takayuki & Fujikoshi, Yasunori, 2010. "High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 101-112, January.
    14. 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.
    15. Schott, James R., 2008. "A test for independence of two sets of variables when the number of variables is large relative to the sample size," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3096-3102, December.

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