On a basic multivariate EIV model with linear equality constraints

Multivariate methods have been widely applied to many practical problems arising in sociology, environmental study, geology, etc. In this paper, we propose an extension of the univariate errors-in-variables model with equality constraints to meet the demand for multivariate cases. We name the multivariate errors-in-variables model with equality constraints CMEIV model here. Here we only consider basic CMEIV which has unique solution. To solve the CMEIV model, TLS (total least squares) principle is applied, and an Euler–Lagrange based approach is adopted to convert it into a nonlinear unconstrained problem. Two kinds of constraints with stochastic and fixed RHS (the right hand side) are considered respectively. The variance–covariance matrices are given in first order approximation along with unbiased estimate of the variance components, as well as the estimate of the unknown parameter matrix.