多层广义潜在空间模型的估计与统计推断
Unfolding and Fusion: Debiased Inference for Generalized Multilayer Latent Space Models
AI总结：
本文提出了一种多层广义潜在空间模型，通过非线性链接函数将多层网络结构表示为张量，并开发了新的展开和融合方法以解决估计和推断问题。
摘要：
多层网络在社会科学、生物学、经济学和国际关系等领域日益普及。尽管应用广泛，但多层网络的推断理论仍不完善。本文提出了一种灵活的潜在空间模型，用于具有多种边类型的多层有向网络，其中每个节点被赋予两个潜在位置，分别捕捉发送和接收行为，而每个层有一个连接矩阵控制该层的结构。通过非线性链接函数，所提出的模型将多层网络的结构表示为张量，这允许进行Tucker低秩分解。这种公式对潜在位置和连接矩阵的估计和统计推断提出了重大挑战，现有技术无法应用。为解决此问题，开发了一种新的展开和融合方法以促进估计。我们建立了估计的潜在位置和连接矩阵的一致性和渐近正态性，这为多层网络应用中的统计推断任务铺平了道路，如构建潜在位置的置信区域以及测试两个网络层是否共享相同的结构。我们通过广泛的模拟研究验证了所提出的方法，并在真实数据上展示了其实际用途。
英文摘要：
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, yet their inferential theory remains underdeveloped. We propose a flexible latent space model for directed multilayer networks with various edge types, where each node has sender and receiver latent positions capturing its sending and receiving behaviors, together with layer-varying out- and in-degree parameters and layer-specific connection matrices. Through nonlinear link functions, the model induces a Tucker low-rank tensor structure in which the structural latent spaces are intertwined with the degree-effect subspaces, creating challenges for estimation and inference. To address these challenges, we develop a novel unfolding and fusion method, coupled with two-sided centering to partial out degree effects. We establish consistency and asymptotic normality for the latent-position estimators. For the connection matrices, we uncover a non-negligible second-order bias induced by fusing two separately estimated unfolding components, derive its explicit representation, and construct a feasible plug-in correction. The resulting debiased estimator is asymptotically normal. Together, these results enable confidence regions for latent positions and tests of whether two network layers share the same structure. Extensive simulation studies validate the proposed method, and a real-world data analysis demonstrates its practical utility.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
