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On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. (English) Zbl 0627.62022
In this paper the authors showed 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 moments of the elements of the sample sums of squares and cross products (SP) matrix exist.

MSC:
62E20 Asymptotic distribution theory in statistics
60F15 Strong limit theorems
62H10 Multivariate distribution of statistics
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