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Fluctuations of the diagonal entries of a large sample precision matrix

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  • Dörnemann, Nina
  • Dette, Holger

Abstract

For a p×n data matrix Xn with i.i.d. centered entries and a population covariance matrix Σ, the corresponding sample precision matrix Σˆ−1 is defined as the inverse of the sample covariance matrix Σˆ=(1/n)Σ1/2XnXn⊤Σ1/2. We determine the joint distribution of a vector of diagonal entries of the matrix Σˆ−1 in the situation, where pn=p

Suggested Citation

  • Dörnemann, Nina & Dette, Holger, 2023. "Fluctuations of the diagonal entries of a large sample precision matrix," Statistics & Probability Letters, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:stapro:v:198:y:2023:i:c:s0167715223000627
    DOI: 10.1016/j.spl.2023.109838
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    References listed on IDEAS

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    1. Sean O’Rourke & David Renfrew & Alexander Soshnikov, 2013. "On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-identically Distributed Entries," Journal of Theoretical Probability, Springer, vol. 26(3), pages 750-780, September.
    2. Jonsson, Dag, 1982. "Some limit theorems for the eigenvalues of a sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 1-38, March.
    3. Anatolyev, Stanislav & Yaskov, Pavel, 2017. "Asymptotics Of Diagonal Elements Of Projection Matrices Under Many Instruments/Regressors," Econometric Theory, Cambridge University Press, vol. 33(3), pages 717-738, June.
    4. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
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