We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of $X$, which, in the case of normal errors, coincides with the maximum likelihood one. We give conditions for asymptotic normality of the estimator when the number of rows in $A$ is increasing. Under mild assumptions, the covariance structure of the limit Gaussian random matrix is nonsingular. For normal errors, the results can be used to construct an asymptotic confidence interval for a linear functional of $X$.

Published at http://dx.doi.org/10.15559/16-VMSTA50 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/). With the Errata