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Exponential bounds for regularized Hotelling’s T2 statistic in high dimension

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  • Issouani, El Mehdi
  • Bertail, Patrice
  • Gautherat, Emmanuelle

Abstract

We obtain exponential inequalities for regularized Hotelling’s Tn2 statistics, that take into account the potential high dimensional aspects of the problem. We explore the finite sample properties of the tail of these statistics by deriving exponential bounds for symmetric distributions and also for general distributions under weak moment assumptions (we never assume exponential moments). For this, we use a penalized estimator of the covariance matrix and propose an optimal choice for the penalty coefficient.

Suggested Citation

  • Issouani, El Mehdi & Bertail, Patrice & Gautherat, Emmanuelle, 2024. "Exponential bounds for regularized Hotelling’s T2 statistic in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000496
    DOI: 10.1016/j.jmva.2024.105342
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2014. "On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 215-228.
    3. Dong, Kai & Pang, Herbert & Tong, Tiejun & Genton, Marc G., 2016. "Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 127-142.
    4. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
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