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Sharp minimax tests for large Toeplitz covariance matrices with repeated observations

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  • Butucea, Cristina
  • Zgheib, Rania

Abstract

We observe a sample of n independent p-dimensional Gaussian vectors with Toeplitz covariance matrix Σ=[σ∣i−j∣]1≤i,j≤p and σ0=1. We consider the problem of testing the hypothesis that Σ is the identity matrix asymptotically when n→∞ and p→∞. We suppose that the covariances σk decrease either polynomially (∑k≥1k2ασk2≤L for α>1/4 and L>0) or exponentially (∑k≥1e2Akσk2≤L for A,L>0).

Suggested Citation

  • Butucea, Cristina & Zgheib, Rania, 2016. "Sharp minimax tests for large Toeplitz covariance matrices with repeated observations," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 164-176.
    • Handle: RePEc:eee:jmvana:v:146:y:2016:i:c:p:164-176
    DOI: 10.1016/j.jmva.2015.09.003
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    References listed on IDEAS

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    Cited by:

    1. Bettache, Nayel & Butucea, Cristina & Sorba, Marianne, 2022. "Fast nonasymptotic testing and support recovery for large sparse Toeplitz covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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