Statistical efficiency of curve fitting algorithms

DOI10.1016/j.csda.2003.11.008zbMath1429.62018arXivcs/0303015OpenAlexW2001617431MaRDI QIDQ957048

C. Lesort, Nikolai I. Chernov

Publication date: 26 November 2008

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cs/0303015

zbMATH Keywords

efficiencycurve fittingfunctional modelleast squares fitalgebraic fitcircle fittingRao-Cramer bound

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Numerical smoothing, curve fitting (65D10)

Related Items (21)

Second-order performance analysis and unbiased estimation for the fitting of concentric circles ⋮ Statistical optimization for geometric fitting: theoretical accuracy bound and high order error analysis ⋮ On the convergence of fitting algorithms in computer vision ⋮ Constrained Cramér-Rao lower bound in errors-in variables (EIV) models: revisited ⋮ A New Perspective in Functional EIV Linear Models: Part II ⋮ On the complexity of curve fitting algorithms ⋮ A doubly optimal ellipse fit ⋮ Semi-doubly optimal concentric circles fitting with presence of heteroscedasticity ⋮ Hyper least squares fitting of circles and ellipses ⋮ Error analysis for circle fitting algorithms ⋮ Further statistical analysis of circle fitting ⋮ A new approach to statistical efficiency of weighted least squares fitting algorithms for reparameterization of nonlinear regression models ⋮ Fast and numerically stable circle fit ⋮ Fitting circles to scattered data: parameter estimates have no moments ⋮ Unified computation of strict maximum likelihood for geometric fitting ⋮ Guaranteed ellipse fitting with a confidence region and an uncertainty measure for centre, axes, and orientation ⋮ Performance evaluation of iterative geometric fitting algorithms ⋮ Fitting circles to data with correlated noise ⋮ Statistical analysis of curve fitting methods in errors-in-variables models ⋮ A comparative study for two newly developed estimators for the slope in the functional EIV linear model ⋮ Parameter estimation techniques: a tutorial with application to conic fitting

Cites Work

• Least-squares fitting by circles
• Cramer-Rao Lower Bounds for Estimation of a Circular Arc Center and Its Radius
• Least-squares fitting of circles and ellipses
• Rationalising the renormalisation method of Kanatani
• Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola
• Heteroscedastic regression in computer vision: Problems with bilinear constraint
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