发表机构
Guanghua School of Management, Peking University; Center for Applied Statistics and School of Statistics, Renmin University of China; School of Statistics and Mathematics, Central University of Finance and Economics（北京大学光华管理学院; 中国人民大学统计学院与应用统计中心; 中央财经大学统计与数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对稀疏网络，提出基于流行度回归的潜空间模型，利用一阶与高阶结构构建四种估计量，并建立渐近理论，实验验证其有效性。
AI 中文摘要
度异质性是网络数据最重要的性质之一。广泛观察到，度异质性通常与节点特征相关。在本研究中，我们探讨了带有节点特征的基于流行度回归的潜空间模型的估计与统计推断。鉴于潜空间模型引发的复杂依赖结构，我们旨在推导出解析上易于处理的目标函数，以有效解释稀疏网络的这种结构。具体而言，我们共提出了四种估计量。前两种估计量仅利用网络的一阶结构（如节点度）开发，而后两种估计量则利用网络的高阶结构（即互惠性和传递性）开发。基于各种非标准U统计量，建立了严格渐近理论。我们发现不同估计量可能具有不同的收敛速率。还讨论了对高阶矩估计量的扩展。为说明目的，进行了大量数值实验以及对作者引文网络链接预测的真实数据分析。
英文摘要
Degree heterogeneity is one of the most important properties of network data. It is widely observed that degree heterogeneity is often related to the nodal features. In this study, we investigate the estimation and statistical inference for a popularity regression-based latent space model with nodal features. Given the complex dependence structure induced by the latent space model, we aim to derive analytically tractable objective functions that effectively account for this structure for sparse networks. Specifically, we propose a total of four estimators. The first two estimators are developed by utilizing only the first-order structure of the network (e.g., the nodal degree), while the last two estimators are developed by leveraging the higher-order network structures (i.e., reciprocity and transitivity). Rigorous asymptotic theory is established based on various non-standard U-statistics. We find that different estimators might have different convergence rates. The extension to higher-order moments-based estimators is also discussed. Extensive numerical experiments and a real data analysis of link prediction for an author citation network are conducted for illustration purposes.
