Estimating the number of significant components in high-dimensional PCA

Abstract

We consider the problem of estimating the number of significant components in high-dimensional principal component analysis ( pca ). We propose a new penalized approach using the explained variance ratio and the rigidity of the nonspiked sample eigenvalues of sample covariance matrices of p variables. Compared with the existing literature, the consistency of the estimator holds not only for independent data but also for some times series data when the dimension p and the sample size n both tend to infinity. Even for independent data it works under weaker conditions including allowing the heterogeneity in the bulk of the population eigenvalues than the existing approaches such as aic and bic . Simulation studies are also conducted to illustrate its good performance.