  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 $X$.
