Least squares methods in maximum likelihood problems
Least squares methods in maximum likelihood problems
复制标题
最大似然问题中的最小二乘法
DOI：
10.1080/10556780600874154
复制
发表时间：
2006
影响因子：
2.2
通讯作者：
M. R. Osborne
中科院分区：
文献类型：
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作者：
M. R. Osborne
求解非线性最小二乘问题的高斯-牛顿算法在独立观测数较多且拟合模型合适的情况下，对求解参数估计问题特别有效。在这种情况下，传统的残差很小的假设是不需要的。高斯-牛顿方法是费雪评分算法的一种特殊情况，用于最大化对数似然，并与此共享许多理想的性质。一般评分算法的线性子问题具有线性最小二乘问题的形式，与一般评分算法的线性子问题具有明显的形式结构对应性。这是一个重要的观察结果，因为它提供了具有计算框架的似然方法，这符合计算正统。线搜索和信任域算法都是可用的，这里对它们进行了比较和对比。结果表明，导致信赖域方法被广泛接受的理论结果类型在直线搜索情况下具有直接等效性，而后者具有更好的变换不变性。连续分布和离散分布的计算实验表明，信赖域方法没有任何优势。
The Gauss–Newton algorithm for solving nonlinear least squares problems proves particularly efficient for solving parameter estimation problems when the number of independent observations is large and the fitted model is appropriate. In this context the conventional assumption that the residuals are small is not needed. The Gauss–Newton method is a special case of the Fisher scoring algorithm for maximizing log likelihoods and shares with this a number of desirable properties. The formal structural correspondence is striking with the linear subproblem for the general scoring algorithm having the form of a linear least squares problem. This is an important observation because it provides likelihood methods with a computational framework, which accords with computational orthodoxy. Both line search and trust region algorithms are available and these are compared and contrasted here. It is shown that the types of theoretical results that have led to the wide acceptance of trust region methods have direct equivalents in the line search case, while the latter have better transformation invariance properties. Computational experiments for both continuous and discrete distributions show no advantage for the trust region approach.
影响因子：
2.1
作者：
通讯作者：
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