Fitting circles to scattered data: parameter estimates have no moments

TL;DR

This paper investigates the statistical properties of circle fitting methods, revealing that under common assumptions, the estimates for circle parameters have infinite moments, which impacts their reliability.

Contribution

It proves that standard circle fitting estimators lack finite moments under typical error distributions, highlighting a fundamental limitation in existing methods.

Findings

Circle parameter estimates have infinite moments under standard assumptions.

Implications for the reliability of circle fitting methods.

Discussion on methodological consequences of infinite moments.

Abstract

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 estimates of the circle center and radius have infinite moments. We also discuss methodological implications of this fact.