加标总体样本协方差矩阵的最大特征值：对角情形
The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case
摘要：
我们考虑大复杂的随机样本协方差矩阵获得的“尖峰人口”，即当真正的协方差矩阵是对角的，但许多特征值等于一。我们研究了当总体和样本容量都变大时最大特征值的极限行为。在样本分布的矩满足一定条件的情况下，证明了最大特征值的渐近涨落与具有相同真协方差的复高斯样本的渐近涨落相同。也考虑了真实的设置。
英文摘要：
We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of the largest eigenvalues when the population and the sample sizes both become large. Under some conditions on moments of the sample distribution, we prove that the asymptotic fluctuations of the largest eigenvalues are the same as for a complex Gaussian sample with the same true covariance. The real setting is also considered.
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