Errors-In-Variables regression and the problem of moments

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...

Full description

Saved in:
Bibliographic Details
Published inBrazilian journal of probability and statistics Vol. 27; no. 4; pp. 401 - 415
Main Authors Al-Sharadqah, Ali, Chernov, Nikolai, Huang, Qizhuo
Format Journal Article
LanguageEnglish
Published Brazilian Statistical Association 01.11.2013
Subjects
Circles
Conic sections
Consistent estimators
Coordinate systems
Ellipses
Estimators
Hyperbolas
Least squares
Maximum likelihood estimation
Parabolas
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0103-0752
2317-6199
DOI:10.1214/11-BJPS173