Maximum likelihood estimation in a multivariate ‘errors in variables’ regression model with unknown error covariance matrix

Abstract

Abstract Two multivariate ‘errors in variables’ regression models are considered which generalize a model proposed by Gleser and Watson by allowing the errors of measurement e and f in the independent and dependent vector variables X and Y, respectively, to have common unknown covariance matrix Σ, rather than Σ = σ2I, as assumed by Gleser and Watson. In the first model, where the parameters are unrestricted, it is shown that maximum likelihood estimators (MLE) for the unknown parameters exist, but that the maximum likelihood equations do not appear to have a closed form solution. In the second model, where the regression matrix B and covariance matrix Σ have common known eigenvectors, MLE’s for the unknown parameters are obtained in closed form, and their consistency properties are investigated. Further, the distribution of, the MLE of B is obtained in this special case using the bivariate noncentral Wishart distribution in the linear case. Keywords: estimationerrors in variables modellinear transformationmultivariatenonoentral Wishartregression