Regression models in which all variables are subject to errors are known as errors-invariables (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).
