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 Np+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.