Consistency of log-likelihood-based information criteria for selecting variables in high-dimensional canonical correlation analysis under nonnormality

The purpose of this paper is to clarify the conditions for consistency of the log-likelihood-based information criteria in canonical correlation analysis of q- and p-dimensional random vectors when the dimension p is large but does not exceed the sample size. Although the vector of observations is assumed to be normally distributed, we do not know whether the underlying distribution is actually normal. Therefore, conditions for consistency are evaluated in a high-dimensional asymptotic framework when the underlying distribution is not normal.