Summary
In this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity. The above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products (SP) matrix exist.
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Research sponsored by the Air Force Office of Scientific Research under Contract F49620-C-0008. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon
The work of this author was done when he was working at the Center for Multivariate Analysis, University of Pittsburgh.
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Yin, Y.Q., Bai, Z.D. & Krishnaiah, P.R. On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Probab. Th. Rel. Fields 78, 509–521 (1988). https://doi.org/10.1007/BF00353874
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DOI: https://doi.org/10.1007/BF00353874