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The Statistical Behaviour of Some Least Squares Estimators of the Centre and Radius of a Circle
Mark Berman,David Culpin +1 more
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In this article, the statistical behavior of some least squares estimators of the center and radius of a circle is examined and the asymptotic consistency of the estimators is investigated.Abstract:
This paper examines the statistical behaviour of some least squares estimators of the centre and radius of a circle. Two error models are used. The asymptotic consistency of the estimators is investigated. Where asymptotic consistency is established, asymptotic covariance matrices are obtained. A small sample simulation study gives results showing the same pattern as those of the asymptotic theory.read more
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Least Squares Fitting of Circles
Nikolai Chernov,C. Lesort +1 more
TL;DR: This work studies the least squares fit (LSF) of circular arcs to incomplete scattered data, analyzes theoretical aspects of the problem, and reveals the cause of unstable behavior of conventional algorithms.
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A Unified View of the Theory of Directional Statistics, 1975-1988
Peter E. Jupp,Kanti V. Mardia +1 more
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Statistical efficiency of curve fitting algorithms
Nikolai Chernov,C. Lesort +1 more
TL;DR: Kanatani's version of the Cramer-Rao lower bound is extended to more general estimates that include many popular algorithms and is shown to be statistically efficient.
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Statistical efficiency of curve fitting algorithms
Nikolai Chernov,C. Lesort +1 more
TL;DR: In this paper, the authors study the problem of fitting parameterized curves to noisy data and derive asymptotic expressions for the bias and the covariance matrix of the parameter estimates under certain assumptions (known as Cartesian and radial functional models).
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Ellipse Fitting with Hyperaccuracy
TL;DR: This paper demonstrates the existence of a "hyperaccurate" method which outperforms ML, made possible by error analysis of ML followed by subtraction of high-order bias terms.
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