标题： 关于使用U统计量进行线性二元交互模型的分析 显示英文标题

标题： On the use of U-statistics for linear dyadic interaction models

摘要： 尽管二元回归在实证应用中被广泛使用，但估计方法的（渐近）性质直到最近才在文献中开始被研究。本文旨在逐步说明如何应用U统计量工具，以获得二元交互两向固定效应模型的成对差异估计量的渐近性质。更具体地说，我们首先提出一种依赖于成对差分的模型估计量，使得固定效应被差分掉。因此，影响函数的求和项将不再是独立的，而是依赖于个体层面，这意味着通常的大数定律和中心极限定理不再直接适用。为克服这些障碍，我们展示了如何将单指标变量的U统计量工具推广到二元数据集的双指标情境。一个关键结果是，对于有向二元结构，可以有不同的方式定义Hajek投影，这将导致不同但等价的一致性渐近方差估计量。本文呈现的结果可以轻松扩展到非线性模型。 显示英文摘要

摘要： Even though dyadic regressions are widely used in empirical applications, the (asymptotic) properties of estimation methods only began to be studied recently in the literature. This paper aims to provide in a step-by-step manner how U-statistics tools can be applied to obtain the asymptotic properties of pairwise differences estimators for a two-way fixed effects model of dyadic interactions. More specifically, we first propose an estimator for the model that relies on pairwise differencing such that the fixed effects are differenced out. As a result, the summands of the influence function will not be independent anymore, showing dependence on the individual level and translating to the fact that the usual law of large numbers and central limit theorems do not straightforwardly apply. To overcome such obstacles, we show how to generalize tools of U-statistics for single-index variables to the double-indices context of dyadic datasets. A key result is that there can be different ways of defining the Hajek projection for a directed dyadic structure, which will lead to distinct, but equivalent, consistent estimators for the asymptotic variances. The results presented in this paper are easily extended to non-linear models.