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Asymptotic power of likelihood ratio tests for high dimensional data

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  • Wang, Cheng

Abstract

This paper studies the asymptotic power of the likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n. The asymptotic distribution under local alternatives is derived and a simulation study is carried out to compare LRT with other tests. All these studies show that LRT is a powerful test to detect small eigenvalues.

Suggested Citation

  • Wang, Cheng, 2014. "Asymptotic power of likelihood ratio tests for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 184-189.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:184-189
    DOI: 10.1016/j.spl.2014.02.010
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    1. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2011. "Asymptotic Power of Sphericity Tests for High-Dimensional Data," Working Papers ECARES ECARES 2011-018, ULB -- Universite Libre de Bruxelles.
    2. Wang, Cheng & Yang, Jing & Miao, Baiqi & Cao, Longbing, 2013. "Identity tests for high dimensional data using RMT," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 128-137.
    3. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    4. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    5. Schott, James R., 2006. "A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 827-843, April.
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    Cited by:

    1. Lin, Ruitao & Liu, Zhongying & Zheng, Shurong & Yin, Guosheng, 2016. "Power computation for hypothesis testing with high-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 10-23.
    2. Badi H. Baltagi & Chihwa Kao & Fa Wang, 2017. "Asymptotic power of the sphericity test under weak and strong factors in a fixed effects panel data model," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 853-882, October.

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