We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that reflects the homophily effect resulting from the nodal attributes or pairwise covariates associated with edges, and a set of latent random noises with unknown distributions. Our interest lies in inferring the unknown degree parameters and homophily parameters. The dimension of the degree parameters increases with the number of nodes. Under the high-dimensional regime, we develop a kernel-based least squares approach to estimate the unknown parameters. The major advantage of our estimator is that it does not encounter the incidental parameter problem for the homophily parameters. We prove consistency of all the resulting estimators of the degree parameters and homophily parameters. We establish high-dimensional central limit theorems for the proposed estimators and provide several applications of our general theory, including testing the existence of degree heterogeneity, testing sparse signals and recovering the support. Simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.

翻译：我们提出了一种用于有向网络中二元链接形成的半参数模型。该模型包含一组衡量节点间受欢迎度或外向性不同效应的度参数、一个反映由节点属性或与边相关的成对协变量所产生的同质性效应的回归参数向量，以及一组具有未知分布的潜在随机噪声。我们的研究重点在于推断未知的度参数和同质性参数。度参数的维度随节点数量增加而增长。在高维体系下，我们开发了一种基于核函数的最小二乘方法来估计未知参数。我们估计量的主要优势在于其不会遇到同质性参数的伴随参数问题。我们证明了所得度参数与同质性参数估计量的一致性。针对所提出的估计量建立了高维中心极限定理，并提供了我们一般理论的若干应用，包括检验度异质性的存在性、检验稀疏信号以及恢复支撑集。通过模拟研究和实际数据应用，展示了所提出方法在有限样本下的性能表现。