, Volume 73, Issue 3, pp 373-384
Date: 01 Sep 2009

Fitting circles to scattered data: parameter estimates have no moments

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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.