This paper studies the asymptotic properties of and improved inference methods for kernel density estimation (KDE) for dyadic data. We first establish novel uniform convergence rates for dyadic KDE under general assumptions. As the existing analytic variance estimator is known to behave unreliably in finite samples, we propose a modified jackknife empirical likelihood procedure for inference. The proposed test statistic is self-normalised and no variance estimator is required. In addition, it is asymptotically pivotal regardless of presence of dyadic clustering. The results are extended to cover the practically relevant case of incomplete dyadic network data. Simulations show that this jackknife empirical likelihood-based inference procedure delivers precise coverage probabilities even under modest sample sizes and with incomplete dyadic data. Finally, we illustrate the method by studying airport congestion.

翻译：本文研究dyadic 数据内核密度估计(KDE)的无症状特性和改良的推断方法。 我们首先在一般假设下为dyadic KDE 设定了新颖的统一合并率。 由于已知现有的分析差异估计器在有限样本中行为不可靠,我们建议修改一个粗便实验概率程序作为推断。 拟议的测试统计数据是自我标准化的,不需要差异估计器。 此外,无论存在 dyadic 群集,它也是同样关键的。 其结果扩大到涵盖不完全的dyadic 网络数据这一实际相关的案例。 模拟表明,这种以实验性概率为基础的概率推断程序提供了精确的覆盖概率, 即使样本大小不大,而且数据不完整。 最后,我们通过研究机场拥挤情况来说明这种方法。