We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses the models which accommodate, for example, transitivity, density-dependent and other stylized features often observed in real network data. By assuming the edges of network at each time are independent conditionally on their lagged values, the models, which exhibit a close connection with temporal ERGMs, facilitate both simulation and the maximum likelihood estimation (MLE) in the straightforward manner. Due to the possible large number of parameters in the models, the initial MLEs may suffer from slow convergence rates. An improved estimator for each component parameter is proposed based on an iteration based on the projection which mitigates the impact of the other parameters (Chang et al., 2021; Chang, Shi and Zhang, 2023). Based on a martingale difference structure, the asymptotic distribution of the improved estimator is derived without the stationarity assumption. The limiting distribution of the estimator is not normal in general, and it reduces to normal when the underlying process satisfies some mixing conditions. Illustration with a transitivity model was carried out in both simulation and with two real network data sets.

主讲人简介：

常晋源，国家杰出青年科学基金获得者，西南财经大学光华特聘教授、中国科学院数学与系统科学研究院研究员、博士生导师。主要从事“超高维数据分析”和“高频金融数据分析”等领域的研究，先后担任统计学和计量经济学国际顶级学术期刊Journalof the Royal Statistical Society Series B、Journal of Business & Economic Statistics以及Joumal of the American Statistical Association的Associate Editor,同时还担任统计学国际一流学术期刊Statistica Sinica的Associate Editor以及管理学中文一流学术期刊《管理科学学报》的领域编辑。已在统计学与计量经济学国际顶级学术期刊Annals of Statistics、Biometrika、Journal of the American Statistical Association、Journal of theRoyal Statistical Society Series B、Journal of Econometrics以及Journal of Business & Economic Statistics上发表论文二十余篇。