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Limiting spectral distribution for a class of random matrices

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  • Yin, Y. Q.
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    Abstract

    Let X = {Xij:i, J = 1, 2,...} be an infinite dimensional random matrix, Tp be a p - p nonnegative definite random matrix independent of X, for p = 1, 2,.... Suppose (1/p) tr Tpk --> Hk a.s. as p --> [infinity] for k = 1, 2,..., and [Sigma]H2k-1/2k

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 20 (1986)
    Issue (Month): 1 (October)
    Pages: 50-68

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    Handle: RePEc:eee:jmvana:v:20:y:1986:i:1:p:50-68

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    Cited by:
    1. Leung, Chi-Ying, 2005. "Regularized classification for mixed continuous and categorical variables under across-location heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 358-374, April.
    2. Glombek, Konstantin, 2013. "A Jarque-Bera test for sphericity of a large-dimensional covariance matrix," Discussion Papers in Statistics and Econometrics 1/13, University of Cologne, Department for Economic and Social Statistics.
    3. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "On the Strong Convergence of the Optimal Linear Shrinkage Estimator for Large Dimensional Covariance Matrix," Papers 1308.2608, arXiv.org, revised Jun 2014.
    4. Yao, Jianfeng, 2012. "A note on a Marčenko–Pastur type theorem for time series," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 22-28.
    5. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2014. "Estimation of the Global Minimum Variance Portfolio in High Dimensions," Papers 1406.0437, arXiv.org.
    6. Rubio, Francisco & Mestre, Xavier, 2011. "Spectral convergence for a general class of random matrices," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 592-602, May.
    7. Pan, Guangming & Miao, Baiqi & Jin, Baisuo, 2008. "Central limit theorem of random quadratics forms involving random matrices," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 804-809, April.
    8. Bai, Z.D. & Miao, Baiqi & Jin, Baisuo, 2007. "On limit theorem for the eigenvalues of product of two random matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 76-101, January.
    9. Olivier Ledoit & Sandrine Péché, 2009. "Eigenvectors of some large sample covariance matrices ensembles," IEW - Working Papers 407, Institute for Empirical Research in Economics - University of Zurich.
    10. Xinghua Zheng & Yingying Li, 2010. "On the estimation of integrated covariance matrices of high dimensional diffusion processes," Papers 1005.1862, arXiv.org, revised Mar 2012.
    11. Jin, Baisuo & Wang, Cheng & Miao, Baiqi & Lo Huang, Mong-Na, 2009. "Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2112-2125, October.
    12. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1330-1338, July.
    13. Bhm, Hilmar & von Sachs, Rainer, 2009. "Shrinkage estimation in the frequency domain of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 913-935, May.

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