Estimating the circle closest to a set of points by maximum likelihood using the BHHH algorithm
Estimating the circle closest to a set of points by maximum likelihood using the BHHH algorithm
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使用 BHHH 算法通过最大似然估计最接近一组点的圆
DOI：
10.1016/j.ejor.2004.09.031
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Caudill
中科院分区：
文献类型：
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作者：
S. Caudill
本文的目的是利用这样的想法：在线性模型中，基于正态性假设的最小二乘估计量和最大似然估计量通常是相同的。特别是，我们希望将正态性假设添加到寻找最佳拟合圆的问题中。添加正态性假设将允许使用 BHHH 算法通过最大似然估计模型。虽然 BHHH 算法不是特别快，但其优点是它只需要对数似然函数的一阶导数，因此比 Newton-Raphson 算法更容易编程。正如我们将要展示的，似然框架还可以轻松测试几个重要的假设并通过回归分析构建 R2 度量。
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 loglikelihood 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 R2measure from regression analysis.