  Principal component analysis (PCA) is the most commonly used statistical
procedure for dimension reduction. An important issue for applying PCA is to
determine the rank, which is the number of dominant eigenvalues of the
covariance matrix. The Akaike information criterion (AIC) and Bayesian
information criterion (BIC) are among the most widely used rank selection
methods. Both use the number of free parameters for assessing model complexity.
In this work, we adopt the generalized information criterion (GIC) to propose a
new method for PCA rank selection under the high-dimensional framework. The GIC
model complexity takes into account the sizes of covariance eigenvalues and can
be better adaptive to practical applications. Asymptotic properties of GIC are
derived and the selection consistency is established under the generalized
spiked covariance model.
