Consistent estimator in multivariate errors-in-variables model in the case of unknown error covariance structure

We consider a linear multivariate errors-in-variables model AX ≈ B, where the matrices A and B are observed with errors and the matrix parameter X is to be estimated. In the case of lack of information about the error covariance structure, we propose an estimator that converges in probability to X as the number of rows in A tends to infinity. Sufficient conditions for this convergence and for the asymptotic normality of the estimator are found. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1026–1033, August, 2007.