Asymptotic properties of canonical correlation analysis for one group with additional observations

We develop canonical correlation analysis in the context of two-step monotone incomplete data drawn from N p + q ( μ , Σ ) , a multivariate normal population with mean μ and covariance matrix Σ . Our data consist of n observations on each group and an additional N − n observations on only one group, where all observations are mutually independent. We perform the canonical correlation analysis using the maximum likelihood estimators, with the monotone incomplete data, of μ and Σ . Further, we derive the asymptotic expansion of the distributions of the canonical correlations and the limiting distributions of the canonical vectors, and we compare them with the results of a typical canonical correlation.