Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices
AbstractResults on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marcenko and Pastur  and Yin , are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles [formula] for most cases of x0 in the boundary of its support. A complete analysis of a way to determine its support, originally outlined in Marcenko and Pastur , is also presented.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 54 (1995)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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.
- Olivier Ledoit & Michael Wolf, 2013. "Optimal estimation of a large-dimensional covariance matrix under Stein’s loss," ECON - Working Papers 122, Department of Economics - University of Zurich.
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- 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 Jul 2013.
- Yao, Jianfeng, 2012. "A note on a Marčenko–Pastur type theorem for time series," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 22-28.
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