Johnstone Iain M
Stanford University and Australian National University.
Aust N Z J Stat. 2018 Mar;60(1):65-74. doi: 10.1111/anzs.12201. Epub 2018 Mar 14.
Consider the classical Gaussian unitary ensemble of size and the real white Wishart ensemble with variables and degrees of freedom. In the limits of large and , with positive ratio in the Wishart case, the expected number of eigenvalues that exit the upper bulk edge is less than one, approaching 0.031 and 0.170 respectively, the latter number being independent of . These statements are consequences of quantitative bounds on tail sums of eigenvalues outside the bulk which are established here for applications in high dimensional covariance matrix estimation.
考虑大小为 的经典高斯酉系综以及具有 个变量和 个自由度的实白 Wishart 系综。在大 和 的极限情况下，在 Wishart 情形中比率 为正，离开上边缘的特征值的期望数量小于 1，分别趋近于 0.031 和 0.170，后一个数字与 无关。这些陈述是关于主体外特征值尾和的定量界的结果，在此建立这些界是为了用于高维协方差矩阵估计。
