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On the overestimation of the largest eigenvalue of a covariance matrix

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  • Soufiane Hayou

Abstract

In this paper, we use a new approach to prove that the largest eigenvalue of the sample covariance matrix of a normally distributed vector is bigger than the true largest eigenvalue with probability 1 when the dimension is infinite. We prove a similar result for the smallest eigenvalue.

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  • Soufiane Hayou, 2017. "On the overestimation of the largest eigenvalue of a covariance matrix," Papers 1708.03551, arXiv.org.
    • Handle: RePEc:arx:papers:1708.03551
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    References listed on IDEAS

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    1. Olivier Ledoit & Michael Wolf, 2003. "Honey, I Shrunk the Sample Covariance Matrix," Working Papers 92, Barcelona School of Economics.
    2. Joong-Ho Won & Johan Lim & Seung-Jean Kim & Bala Rajaratnam, 2013. "Condition-number-regularized covariance estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 427-450, June.
    3. Joel Bun & Jean-Philippe Bouchaud & Marc Potters, 2016. "Cleaning large correlation matrices: tools from random matrix theory," Papers 1610.08104, arXiv.org.
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