A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits of the sample spiked eigenvalues where the population covariance matrices are arbitrary which successively removed an unrealistic condition posed in the previous works, that is, the covariance matrices are assumed to be diagonal or diagonal block-wise structure. In addition, we also give a consistent estimator of the population spiked eigenvalues. A series of simulations are conducted that support the theoretical results and illustrate the accuracy of our estimators.

本文考虑了广义的尖峰费舍尔矩阵。我们建立了描述高维广义Fisher矩阵极限频谱分布支持的标准，并研究了样本加标特征值的几乎确定的极限，其中种群协方差矩阵是任意的，从而相继消除了先前提出的不切实际的条件。的工作原理，即协方差矩阵被假定为对角或对角逐块结构。此外，我们还给出了人口峰值特征值的一致估计。进行了一系列模拟，以支持理论结果并说明我们估计量的准确性。