Consistency of the structured total least squares estimator in a multivariate errors-in-variables model

Kukush, A., Markovsky, I. and Van Huffel, S. (2005) Consistency of the structured total least squares estimator in a multivariate errors-in-variables model. Journal of Statistical Planning and Inference, 133, (2), 315-358.


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The structured total least squares estimator, defined via a constrained optimization problem, is a generalization of the total least squares estimator when the data matrix and the applied correction satisfy given structural constraints. In the paper, an affine structure with additional assumptions is considered. In particular, Toeplitz and Hankel structured, noise free and unstructured blocks are allowed simultaneously in the augmented data matrix. An equivalent optimization problem is derived that has as decision variables only the estimated parameters. The cost function of the equivalent problem is used to prove consistency of the structured total least squares estimator. The results for the general affine structured multivariate model are illustrated by examples of special models. Modification of the results for block-Hankel/Toeplitz structures is also given. As a by-product of the analysis of the cost function, an iterative algorithm for the computation of the structured total least squares estimator is proposed.

Item Type: Article
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Keywords: block-Hankel/Toeplitz structure, consistency, dynamic errors-in-variables model, iterative algorithm, structured total least squares, total least squares.
Divisions : Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Southampton Wireless Group
ePrint ID: 263296
Accepted Date and Publication Date:
Date Deposited: 06 Jan 2007
Last Modified: 31 Mar 2016 14:07
Further Information:Google Scholar

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