报告题目：  Autoregressive Networks

报 告 人：  栗家量

时    间：  2023年9月27日(周三)下午3:30-5:30

地    点：  西安交通大学创新港涵英楼经济金融研究院8004报告厅

报告人简介：

栗家量，新加坡国立大学统计与应用概率系教授，于2006年在美国威斯康星大学麦迪逊分校获得统计学博士学位。研究方向包括金融统计、统计学习、 生存分析等。研究成果发表于Annals of Statistics, Journal of the American Statistical Association, Journal of the Royal Statistical Society Series B, Journal of Econometrics等顶级期刊,并著有专著1本。栗家量教授是美国统计学会（ASA）Fellow，美国数理统计协会（IMS）Fellow,国际统计协会（ISI）Elected Member。担任Annals of Applied Statistics、Biostatistics & Epidemiology和Lifetime Data Analysis等国际权威期刊的副主编。

摘要：

We propose a first-order autoregressive (i.e. AR (1)) model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and efficient statistical inference methods including a permutation test for diagnostic checking for the fitted network models. The proposed model can be applied to the network processes with various underlying structures but with independent edges. As an illustration, an AR (1) stochastic block model has been investigated in depth, which characterizes the latent communities by the transition probabilities over time. This leads to a new and more effective spectral clustering algorithm for identifying the latent communities. We have derived a finite sample condition under which the perfect recovery of the community structure can be achieved by the newly defined spectral clustering algorithm. Furthermore, the inference for a change point is incorporated into the AR (1) stochastic block model to cater for possible structure changes. We have derived the explicit error rates for the maximum likelihood estimator of the change-point. Application with three real data sets illustrates both relevance and usefulness of the proposed AR (1) models and the associate inference methods.

经济与金融学院

2023年9月22日