Fitting circles to scattered data: parameter estimates have no moments

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...

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Bibliographic Details
Published in:	Metrika Vol. 73; no. 3; pp. 373 - 384
Main Author:	Chernov, N.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01-05-2011
Subjects:	Economic Theory/Quantitative Economics/Mathematical Methods Mathematics and Statistics Probability Theory and Stochastic Processes Statistics Orthogonal regression Moments of estimates Errors-in-variables Least squares fit Circle fitting
Online Access:	Get full text
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Summary:	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.
ISSN:	0026-1335 1435-926X
DOI:	10.1007/s00184-009-0283-y