Estimating the circle closest to a set of points by maximum likelihood using the Berndt, Hall, Hall and Hausman (BHHH) algorithm

The purpose of this paper is to exploit the idea that, in linear models, the least-squares estimators and the maximum likelihood estimators based on the normality assumption are often identical. In particular, we wish to add the normality assumption to the problem of finding the best fitting circle. The addition of the normality assumption will allow the use of the BHHH algorithm to estimate the model by maximum likelihood. Although the BHHH algorithm is not especially fast, its virtue is that it only requires the first derivatives of the log-likelihood function and is therefore easier to program than the Newton–Raphson algorithm. As we will show, the likelihood framework also allows for easy testing of several important hypotheses and construction of an R² measure from regression analysis.