标题： 可识别性在无链接线性回归中的某些结果和开放问题 显示英文标题

标题： Identifiability in Unlinked Linear Regression: Some Results and Open Problems

摘要： 经典线性回归问题中的一个隐含假设是完全了解协变量和响应之间的现有联系。 在未链接线性回归（ULR）中，这种联系可能是部分或完全缺失的。 虽然导致这种缺失的原因可能不同，但在统计推断中一个共同的挑战是回归参数的潜在不可识别性。 在本说明中，我们回顾了当协变量向量的$d \ge 2$成分独立同分布时的可识别性现有文献。 当这些成分具有不同的分布时，我们证明在一般情况下无法证明类似的定理。 然而，我们在对$d \ge 2$的额外参数假设下或在$d=2$的情况下对四阶矩的条件下的情况下，证明了一些可识别性结果。 最后，我们将ULR与已建立的独立成分分析（ICA）领域之间的一些有趣联系进行了阐述。 显示英文摘要

摘要： A tacit assumption in classical linear regression problems is the full knowledge of the existing link between the covariates and responses. In Unlinked Linear Regression (ULR) this link is either partially or completely missing. While the reasons causing such missingness can be different, a common challenge in statistical inference is the potential non-identifiability of the regression parameter. In this note, we review the existing literature on identifiability when the $d \ge 2$ components of the vector of covariates are independent and identically distributed. When these components have different distributions, we show that it is not possible to prove similar theorems in the general case. Nevertheless, we prove some identifiability results, either under additional parametric assumptions for $d \ge 2$ or conditions on the fourth moments in the case $d=2$. Finally, we draw some interesting connections between the ULR and the well established field of Independent Component Analysis (ICA).