Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices
Abstract
Let X be n - N containing i.i.d. complex entries with E X11 - EX112 = 1, and T an n - n random Hermitian nonnegative definite, independent of X. Assume, almost surely, as n --> [infinity], the empirical distribution function (e.d.f.) of the eigenvalues of T converges in distribution, and the ratio n/N tends to a positive number. Then it is shown that, almost surely, the e.d.f. of the eigenvalues of (1/N) XX*T converges in distribution. The limit is nonrandom and is characterized in terms of its Stieltjes transform, which satisfies a certain equation.Download Info
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Bibliographic Info
Article provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 55 (1995)
Issue (Month): 2 (November)
Pages: 331-339
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Wenjie Wang, 2012. "Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments," KIER Working Papers 810, Kyoto University, Institute of Economic Research.
- Robert, Christian Y. & Rosenbaum, Mathieu, 2010. "On the limiting spectral distribution of the covariance matrices of time-lagged processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2434-2451, November.
- Olivier Ledoit & Michael Wolf, 2013. "Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions," ECON - Working Papers 105, Department of Economics - University of Zurich, revised Mar 2013.
- 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.
- Dozier, R. Brent & Silverstein, Jack W., 2007. "On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 678-694, April.
- 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.
- Bai, Z.D. & Zhang, L.X., 2010. "The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1927-1949, October.
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