Errors-In-Variables regression and the problem of moments

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