发表机构
The University of Tokyo; National Institute of Infectious Diseases, Japan（东京大学; 日本国立感染症研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对线性结构方程模型的有理因果估计，发现部分分母的自归一化特性，给出因子与秩准则分类分母，验证线性前门调整的Wald推断有效性，模拟与真实数据区分不同诊断的覆盖率表现。
AI 中文摘要
线性结构方程模型中的有理因果估计量采用一个协方差多项式除以另一个的形式，小分母通常被解释为弱识别。我们证明，在高斯抽样下，部分分母在一阶时无法进入该 regime，它们的抽样变异与其大小完全成正比，因此标准化分母在每个样本中都是常数。嵌套协方差子式的幂次乘积在所有维度上都具有该性质，并允许存在精确的 Wishart 枢轴。在二维情况下，逆问题是完全的；在三维情况下，一个混合族仍未解决，而因子与秩准则可对所有带有线性或二次无行列式因子的分母进行分类，涵盖工具变量、前门和后门公式。对于线性前门调整，即使中介变量残差方差以任意速率消失，只要处理-中介变量系数非零，Wald 推断仍渐近有效。模拟结果显示，当朴素处理-代理诊断增强时，代理 Wald 覆盖率下降，而前门覆盖率保持名义水平，右心导管插入术数据可区分朴素诊断与分母相关诊断。
英文摘要
Many estimators are ratios of coprime polynomials in a sample covariance matrix, and their accuracy depends on the relative fluctuation of the sample denominator. Under Gaussian sampling in fixed dimension, we call a nonconstant polynomial denominator self-normalizing if the first-order variance of its relative error does not depend on the population covariance. We prove that these denominators are exactly the flag powers, nonzero constant multiples of products of positive integer powers of nested generalized variances. Equivalently, the denominator's sample-to-population ratio has a covariance-independent finite-sample law, which we determine explicitly. Sufficiency is classical; the new converse shows that a first-order variance condition forces an exact sampling law. We show that relative stability, meaning bounded first-order relative variance, characterizes uniform tightness of scaled relative errors over positive-definite covariances. It permits replacing the sample denominator by its population value in the limit theory of the ratio. Self-normalization is its rigid core. We locate these classes in applications, where regression on predecessors in a fixed order yields only constant or self-normalizing denominators, instrumental-variable formulas yield relatively unstable ones, and nonparametric identifiability does not guarantee relative stability.
