Asymptotic Properties of the Estimators for Multivariate Components of Variance

S. Remadi and Y. Amemiya

Journal of Multivariate Analysis, 1994, vol. 49, issue 1, 110-131

Abstract: Estimation of the covariance matrices in the multivariate balanced one-way random effect model is discussed. The rank of the between-group covariance matrix plays a large role in model building as well as in assessing asymptotic properties of the estimated covariance matrices. The restricted (residual) maximum likelihood estimators derived under a rank condition are considered. Asymptotic properties of the estimators are derived for a possibly incorrectly specified rank and under either the number of groups, the number of replicates, or both, tending to infinity. A higher order expansion covering various cases leads to a common approximate inference procedure which can be used in a wide range of practical situations. A simulation study is also presented.

Date: 1994
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