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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Statistical analysis of curve fitting methods in errors-in-variables models


Authors: A. Al-Sharadqah and N. Chernov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 1-14
MSC (2010): Primary 62H10, 62J02; Secondary 62H35
Published electronically: July 26, 2012
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Abstract: Regression models in which all variables are subject to errors are known as errors-in-variables (EIV) models. The respective parameter estimates have many unusual properties: their exact distributions are very hard to determine, and their absolute moments are often infinite (so that their mean and variance do not exist). In our paper, Error analysis for circle fitting algorithms, Electr. J. Stat. 3 (2009), 886-911, we developed an unconventional statistical analysis that allowed us to effectively assess EIV parameter estimates and design new methods with superior characteristics. In this paper we validate our approach in a series of numerical tests. We also prove that in the case of fitting circles, the estimates of the parameters are absolutely continuous (have densities).


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Additional Information

A. Al-Sharadqah
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
Email: alsha1aa@gmail.com

N. Chernov
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
Email: chernov@math.uab.edu

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00860-0
PII: S 0094-9000(2012)00860-0
Keywords: Errors-in-variables, regression, curve fitting, circle fitting, line fitting, functional model
Received by editor(s): March 4, 2010
Published electronically: July 26, 2012
Additional Notes: The second author was partially supported by National Science Foundation, grant DMS-0652896
Article copyright: © Copyright 2012 American Mathematical Society