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Original Articles

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

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Pages 325-348 | Published online: 06 Feb 2019
 

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 Np+q(μ,Σ), which is a multivariate normal population with mean μ and covariance matrix Σ. Our data consist of n observations of all p + q variables and an additional Nn 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 Σ. 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.

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