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Biometrika 1983 70(1):263-267; doi:10.1093/biomet/70.1.263
© 1983 by Biometrika Trust
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Estimation of multivariate linear functional relationships

N. N. CHAN and T. K. MAX

Department of Mathematics, Chinese University of Hong Kong Hong Kong
Department of Statistics, University of Hong Kong Hong Kong

Consistent estimation of the structural parameters in a multivariate linear functional relationship between two vector variables observed with error is considered. When the covariance matrix of the error terms contains unknown parameters, it is shown that the usual maximum likelihood approach generally yields inconsistent estimators. A natural modification of the likelihood equations leading to a consistent estimation procedure is proposed. The connexion with estimation in the corresponding structural relationship model is also considered.

Key Words: Consistency • Maximum likelihood • Multivariate functional relationship • Structural relationship


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