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Consistent estimation in an implicit quadratic measurement error model

Consistent estimation in an implicit quadratic measurement error model
Consistent estimation in an implicit quadratic measurement error model
An adjusted least squares estimator is derived that yields a consistent estimate of the parameters of an implicit quadratic measurement error model. In addition, a consistent estimator for the measurement error noise variance is proposed. Important assumptions are: (1) all errors are uncorrelated identically distributed and (2) the error distribution is normal. The estimators for the quadratic measurement error model are used to estimate consistently conic sections and ellipsoids. Simulation examples, comparing the adjusted least squares estimator with the ordinary least squares method and the orthogonal regression method, are shown for the ellipsoid fitting problem.
Adjusted least squares, Conic fitting, Consistent estimator, Ellipsoid fitting, Quadratic measurement error model.
0167-9473
123-147
Kukush, A.
9cf76e13-c463-47c3-9467-0ae6b04df4ef
Markovsky, I.
3e68743b-f22e-4b2b-b1a8-2ba4eb036a69
Van Huffel, S.
e64be3d0-00e1-4900-ab8e-74aed4792678
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. (2004) Consistent estimation in an implicit quadratic measurement error model. Computational Statistics & Data Analysis, 47 (1), 123-147. (doi:10.1016/j.csda.2003.10.022).

Record type: Article

Abstract

An adjusted least squares estimator is derived that yields a consistent estimate of the parameters of an implicit quadratic measurement error model. In addition, a consistent estimator for the measurement error noise variance is proposed. Important assumptions are: (1) all errors are uncorrelated identically distributed and (2) the error distribution is normal. The estimators for the quadratic measurement error model are used to estimate consistently conic sections and ellipsoids. Simulation examples, comparing the adjusted least squares estimator with the ordinary least squares method and the orthogonal regression method, are shown for the ellipsoid fitting problem.

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More information

Published date: 1 August 2004
Keywords: Adjusted least squares, Conic fitting, Consistent estimator, Ellipsoid fitting, Quadratic measurement error model.
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 263294
URI: https://eprints.soton.ac.uk/id/eprint/263294
ISSN: 0167-9473
PURE UUID: c1355b98-7142-426b-870d-8a60840a333c

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Date deposited: 06 Jan 2007
Last modified: 19 Jul 2019 22:29

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