Consistent estimation in the bilinear multivariate errors-in-variables model
Consistent estimation in the bilinear multivariate errors-in-variables model
A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A?Rm×n, B?Rp×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case. An adjusted least squares estimator hat X is constructed, which converges to the true value X, as m -> infty, q -> infty. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study.
bilinear multivariate measurement error models, errors-in-variables models, adjusted least squares, consistency, asymptotic normality, small sample modification.
253-285
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
2003
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
Kukush, A., Markovsky, I. and Van Huffel, S.
(2003)
Consistent estimation in the bilinear multivariate errors-in-variables model.
Metrika, 57 (3), .
Abstract
A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A?Rm×n, B?Rp×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case. An adjusted least squares estimator hat X is constructed, which converges to the true value X, as m -> infty, q -> infty. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study.
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Published date: 2003
Keywords:
bilinear multivariate measurement error models, errors-in-variables models, adjusted least squares, consistency, asymptotic normality, small sample modification.
Organisations:
Southampton Wireless Group
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Local EPrints ID: 263292
URI: http://eprints.soton.ac.uk/id/eprint/263292
PURE UUID: 038b04a8-42c6-4196-ab40-e2d9febd79cc
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Date deposited: 06 Jan 2007
Last modified: 14 Mar 2024 07:28
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Author:
A. Kukush
Author:
I. Markovsky
Author:
S. Van Huffel
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