, Volume 73, Issue 3, pp 373–384

Fitting circles to scattered data: parameter estimates have no moments


DOI: 10.1007/s00184-009-0283-y

Cite this article as:
Chernov, N. Metrika (2011) 73: 373. doi:10.1007/s00184-009-0283-y


We study a nonlinear regression problem of fitting a circle (or a circular arc) to scattered data. We prove that under any standard assumptions on the statistical distribution of errors that are commonly adopted in the literature, the orthogonal regression estimators of the circle center and radius have infinite (absolute) moments. We also discuss methodological implications of this fact.


Orthogonal regressionErrors-in-variablesLeast squares fitCircle fittingMoments of estimates

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA