Errors-In-Variables regression and the problem of moments

Abstract

In regression problems where covariates are subject to errors (albeit small) it often happens that maximum likelihood estimators (MLE) of relevant parameters have infinite moments. We study here circular and elliptic regression, that is, the problem of fitting circles and ellipses to observed points whose both coordinates are measured with errors. We prove that several popular circle fits due to Pratt, Taubin, and others return estimates of the center and radius that have infinite moments. We also argue that estimators of the ellipse parameters (center and semiaxes) should have infinite moments, too.