Asymptotic Eigenvalue Curves of Random Covariance Matrices

摘要

In recent years the principal component decomposition of large data sets has been facilitated by Monte Carlo experiments that provide random eigenvalue reference curves against which real data eigenvalue curves could be compared for statistical significance. When data sets are very large, the Monte Carlo simulations can become extensive, and in their stead recourse to the following analytical formulas, tables, and graphs may be made. These will allow a first examination of the data set's eigenvalue curve for possible statistical significance.