Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model
Volume 3, Issue 1 (2016), pp. 47–57
Pub. online: 29 March 2016
Type: Research Article
Open Access
Open Access
Received
11 February 2016
11 February 2016
Revised
7 March 2016
7 March 2016
Accepted
11 March 2016
11 March 2016
Published
29 March 2016
29 March 2016
Abstract
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.
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