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A note on the largest eigenvalue of a large dimensional sample covariance matrix

Author

Listed:
  • Bai, Z. D.
  • Silverstein, Jack W.
  • Yin, Y. Q.

Abstract

Let {vij; i, J = 1, 2, ...} be a family of i.i.d. random variables with E(v114) = [infinity]. For positive integers p, n with p = p(n) and p/n --> y > 0 as n --> [infinity], let Mn = (1/n) Vn VnT , where Vn = (vij)1

Suggested Citation

  • Bai, Z. D. & Silverstein, Jack W. & Yin, Y. Q., 1988. "A note on the largest eigenvalue of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 166-168, August.
    • Handle: RePEc:eee:jmvana:v:26:y:1988:i:2:p:166-168
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    Cited by:

    1. Hugo Freeman & Martin Weidner, 2021. "Low-rank approximations of nonseparable panel models," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 40-77.
    2. Yumou Qiu & Song Xi Chen, 2015. "Bandwidth Selection for High-Dimensional Covariance Matrix Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1160-1174, September.
    3. Qiu, Yumou & Chen, Songxi, 2012. "Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation," MPRA Paper 46242, University Library of Munich, Germany.
    4. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    5. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    6. Sokbae Lee & Serena Ng, 2020. "An Econometric Perspective on Algorithmic Subsampling," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 45-80, August.
    7. Li, Yuling & Zhou, Huanchao & Hu, Jiang, 2023. "The eigenvector LSD of information plus noise matrices and its application to linear regression model," Statistics & Probability Letters, Elsevier, vol. 197(C).
    8. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    9. Onatski, A., 2018. "Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise," Cambridge Working Papers in Economics 1808, Faculty of Economics, University of Cambridge.
    10. Ningning Xia & Zhidong Bai, 2015. "Functional CLT of eigenvectors for large sample covariance matrices," Statistical Papers, Springer, vol. 56(1), pages 23-60, February.
    11. Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
    12. Heiny, Johannes & Mikosch, Thomas, 2018. "Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2779-2815.
    13. Peng, Liuhua & Chen, Song Xi & Zhou, Wen, 2016. "More powerful tests for sparse high-dimensional covariances matrices," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 124-143.
    14. Han Xiao & Wang Zhou, 2010. "Almost Sure Limit of the Smallest Eigenvalue of Some Sample Correlation Matrices," Journal of Theoretical Probability, Springer, vol. 23(1), pages 1-20, March.
    15. Jiti Gao & Xiao Han & Guangming Pan & Yanrong Yang, 2014. "High Dimensional Correlation Matrices: CLT and Its Applications," Monash Econometrics and Business Statistics Working Papers 26/14, Monash University, Department of Econometrics and Business Statistics.
    16. Pan, Guangming & Zhou, Wang, 2010. "Circular law, extreme singular values and potential theory," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 645-656, March.
    17. M. Capitaine, 2013. "Additive/Multiplicative Free Subordination Property and Limiting Eigenvectors of Spiked Additive Deformations of Wigner Matrices and Spiked Sample Covariance Matrices," Journal of Theoretical Probability, Springer, vol. 26(3), pages 595-648, September.
    18. Martin, Ian W.R. & Nagel, Stefan, 2022. "Market efficiency in the age of big data," Journal of Financial Economics, Elsevier, vol. 145(1), pages 154-177.
    19. Bai, Zhidong & Silverstein, Jack W., 2022. "A tribute to P.R. Krishnaiah," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    20. Auffinger, Antonio & Tang, Si, 2016. "Extreme eigenvalues of sparse, heavy tailed random matrices," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3310-3330.
    21. Greenaway-McGrevy, Ryan & Han, Chirok & Sul, Donggyu, 2012. "Asymptotic distribution of factor augmented estimators for panel regression," Journal of Econometrics, Elsevier, vol. 169(1), pages 48-53.
    22. Heiny, Johannes & Mikosch, Thomas, 2017. "Eigenvalues and eigenvectors of heavy-tailed sample covariance matrices with general growth rates: The iid case," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2179-2207.
    23. Kamil Jurczak, 2015. "A Universal Expectation Bound on Empirical Projections of Deformed Random Matrices," Journal of Theoretical Probability, Springer, vol. 28(2), pages 650-666, June.
    24. Shizhe Hong & Haiyan Song & Jiang Hu & Zhidong Bai, 2025. "A Note on the Convergence of the Extreme Eigenvalues of a Large-Dimensional Sample Covariance Matrix," Journal of Theoretical Probability, Springer, vol. 38(2), pages 1-16, June.

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