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Asymptotic Properties for the Eigenvalue and Eigenvector of a Covariance Matrix under Two-Step Monotone Incomplete Multivariate Normal Data

SYNOPTIC ABSTRACT We derive the asymptotic properties for the eigenvalue and eigenvector of a covariance matrix in the context of two-step monotone incomplete data drawn from , which is a multivariate normal population with mean and covariance matrix . Our data consist of n observations of all p + q variables and an additional N – n observations of the first p variables; all observations are mutually independent. We use a maximum likelihood estimator (MLE) and an unbiased estimator (UBE) for a covariance matrix . Furthermore, we correct for bias of the eigenvalue and eigenvector by evaluating asymptotic expectations. Finally, we investigate the accuracy of our results using numerical simulations.