The limits of the sample spiked eigenvalues for a high-dimensional generalized Fisher matrix and its applications

Abstract

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.

arXiv comment21 pages, 36 figures

References in corpus (8)

• PCA consistency in high dimension, low sample size context
• Optimal detection of sparse principal components in high dimension
• Limit theorems for sample eigenvalues in a generalized spiked population model
• Asymptotics of Empirical Eigen-structure for Ultra-high Dimensional Spiked Covariance Model
• Surprising Asymptotic Conical Structure in Critical Sample Eigen-Directions
• Limiting Laws for Divergent Spiked Eigenvalues and Largest Non-spiked Eigenvalue of Sample Covariance Matrices
• Generalized Four Moment Theorem and an Application to CLT for Spiked Eigenvalues of Large-dimensional Covariance Matrices
• CLT for large dimensional general Fisher matrices and its applications in high-dimensional data analysis