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Limiting spectral distribution for a class of random matrices


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  • Yin, Y. Q.
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    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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    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. Rubio, Francisco & Mestre, Xavier, 2011. "Spectral convergence for a general class of random matrices," Statistics & Probability Letters, Elsevier, Elsevier, vol. 81(5), pages 592-602, May.
    2. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2014. "Estimation of the Global Minimum Variance Portfolio in High Dimensions," Papers 1406.0437,
    3. Leung, Chi-Ying, 2005. "Regularized classification for mixed continuous and categorical variables under across-location heteroscedasticity," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 93(2), pages 358-374, April.
    4. Pan, Guangming & Miao, Baiqi & Jin, Baisuo, 2008. "Central limit theorem of random quadratics forms involving random matrices," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(6), pages 804-809, April.
    5. 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,, revised Jun 2014.
    6. Yao, Jianfeng, 2012. "A note on a Marčenko–Pastur type theorem for time series," Statistics & Probability Letters, Elsevier, Elsevier, vol. 82(1), pages 22-28.
    7. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 101(6), pages 1330-1338, July.
    8. 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, Elsevier, vol. 100(9), pages 2112-2125, October.
    9. 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, Elsevier, vol. 98(1), pages 76-101, January.
    10. Xinghua Zheng & Yingying Li, 2010. "On the estimation of integrated covariance matrices of high dimensional diffusion processes," Papers 1005.1862,, revised Mar 2012.
    11. 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.
    12. Bhm, Hilmar & von Sachs, Rainer, 2009. "Shrinkage estimation in the frequency domain of multivariate time series," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(5), pages 913-935, May.
    13. 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.


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