Fitting circles to scattered data: parameter estimates have no moments

Details Fitting circles to scattered data: parameter estimates have no moments Fitting circles to scattered data: parameter estimates have no moments

2009-07-02

arxiv.org/abs/0907.0429v1

Mathematics

Statistics Theory

14 pages

Scientific paper

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.

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