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Likelihood ratio tests for many groups in high dimensions

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  • Dette, Holger
  • Dörnemann, Nina

Abstract

In this paper, we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the logarithm of various test statistics and compare our results with the approximations obtained from a central limit theorem where the number of groups is fixed.

Suggested Citation

  • Dette, Holger & Dörnemann, Nina, 2020. "Likelihood ratio tests for many groups in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:jmvana:v:178:y:2020:i:c:s0047259x1930346x
    DOI: 10.1016/j.jmva.2020.104605
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    References listed on IDEAS

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    1. Dette, Holger & Tomecki, Dominik, 2019. "Determinants of block Hankel matrices for random matrix-valued measures," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5200-5235.
    2. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
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    4. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.
    5. Karl Bruce Gregory & Raymond J. Carroll & Veerabhadran Baladandayuthapani & Soumendra N. Lahiri, 2015. "A Two-Sample Test for Equality of Means in High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 837-849, June.
    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. Tiefeng Jiang & Yongcheng Qi, 2015. "Likelihood Ratio Tests for High-Dimensional Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 988-1009, December.
    8. A. M. Hanea & G. F. Nane, 2018. "The asymptotic distribution of the determinant of a random correlation matrix," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(1), pages 14-33, February.
    9. Li, Weiming & Qin, Yingli, 2014. "Hypothesis testing for high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 108-119.
    10. 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.
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    Cited by:

    1. Mingyue Hu & Yongcheng Qi, 2023. "Limiting distributions of the likelihood ratio test statistics for independence of normal random vectors," Statistical Papers, Springer, vol. 64(3), pages 923-954, June.
    2. Dörnemann, Nina, 2023. "Likelihood ratio tests under model misspecification in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    3. Loubaton, Philippe & Rosuel, Alexis & Vallet, Pascal, 2023. "On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    4. Gusakova, Anna & Heiny, Johannes & Thäle, Christoph, 2023. "The volume of random simplices from elliptical distributions in high dimension," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 357-382.
    5. Bodnar, Taras & Parolya, Nestor & Thorsén, Erik, 2023. "Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?," Finance Research Letters, Elsevier, vol. 54(C).

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