Estimation of Covariances between Observed Variables in Factor Analysis

Estimation of the covariance between two of the variables in a set of observed variables is investigated when the factor analysis model holds. Under the assumption of multivariate normality, explicit formulae for the asymptotic sampling variances and covariances of the maximum likelihood estimators are derived. Asymptotic sampling variances of functions of the covariances are also investigated. Examples suggest that while the usual unbiased estimators can perform poorly in estimating the covariances, they may perform to the same extent as the maximum likelihood estimators in estimating functions of the covariances.