具有相关误差的递归线性模型的最大似然估计的计算
Computing maximum likelihood estimates in recursive linear models with correlated errors
摘要：
在递归线性模型中，所有变量的多元正态联合分布表现出由线性结构方程的递归（或非循环）系统诱导的相关结构。这些线性模型有着悠久的传统，出现在看似无关的回归、结构方程建模和因果推理方法中。它们还通过称为路径图的经典表示与高斯图形模型相关。尽管这些模式有着悠久的历史，但仍存在一些问题。在本文中，我们解决的问题，计算最大似然估计的子类中的“弓自由”递归线性模型。术语“无弓形”是指如果变量$j$的结构方程中出现变量$i$，则变量$i$和$j$的误差不相关的条件。我们介绍了一种新的算法，称为残差迭代条件拟合（RICF），可以实现仅使用最小二乘计算。与现有算法相比，RICF具有清晰的收敛性，并尽可能以封闭形式找到参数估计。
英文摘要：
In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structural equations. These linear models have a long tradition and appear in seemingly unrelated regressions, structural equation modelling, and approaches to causal inference. They are also related to Gaussian graphical models via a classical representation known as a path diagram. Despite the models' long history, a number of problems remain open. In this paper, we address the problem of computing maximum likelihood estimates in the subclass of `bow-free' recursive linear models. The term `bow-free' refers to the condition that the errors for variables $i$ and $j$ be uncorrelated if variable $i$ occurs in the structural equation for variable $j$. We introduce a new algorithm, termed Residual Iterative Conditional Fitting (RICF), that can be implemented using only least squares computations. In contrast to existing algorithms, RICF has clear convergence properties and finds parameter estimates in closed form whenever possible.
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