Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 3, 409--435

MIVQUE and Maximum Likelihood Estimation for Multivariate Linear Models with Incomplete Observations

David Causeur, Laboratoire de Math\'{e}matiques Appliqu\'{e}es, Rennes, France

SUMMARY. The problem of estimating the parameters of multivariate linear models in the context of an arbitrary pattern of missing data is addressed in the present paper. While this problem is frequently handled by EM strategies, we propose a Gauss-Markov approach based on an initial linearization of the covariance of the model. A complete class of quadratic estimators is first exhibited in order to derive locally Minimum Variance Quadratic Unbiased Estimators (MIVQUE) of the variance parameters. Apart from the interest in locally MIVQUE itself, this approach gives more insight into maximum likelihood estimation. Indeed, an iterated version of MIVQUE is proposed as an alternative to EM to calculate the maximum likelihood estimators. Finally, MIVQUE and maximum likelihood estimation are compared by simulations.

AMS (2000) subject classification. Primary 62F10, 62J05.

Key words and phrases. Incomplete observations, MIVQUE, multivariate linear models.

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