统计与管理学院2016年学术报告14期

【主  题】On the Estimation of the Preferential Attachment Network Model and more

【报告人】 Fengnan Gao

Leiden University, The Netherlands

【时  间】 2016年4月28日（星期四）09:00－10:00

【地  点】 上海财经大学统计与管理学院大楼1208室

【摘  要】 The preferential attachment (PA) network is a popular way of modeling the social networks, the collaboration networks and etc. The PA network model is an evolving network where new nodes keep coming in. When a new node comes in, it establishes only one connection with an existing node. The random choice on the existing node is via a multinomial distribution with probability weights based on a preferential function $f$ on the degrees. $f$ is assumed apriori non-decreasing, which means the nodes with high degrees are more likely to get new connections, i.e. "the rich get richer". We proposed an estimator on $f$, that maps the natural numbers to the positive real line. We show, with techniques from branching process, our estimator is consistent. If $f$ is affine, meaning $f(k) = k + delta$, it is well known that such a model leads to a  power-law degree distribution. We proposed a maximum likelihood estimator for $\delta$ and establish a central limit result on the MLE of $delta$.  If $f$ belongs to a parametric family not faster than linear, we show the MLE will also yield optimal performance with the result of asymptotic normality.  If possible, we will also talk about the potential extensions of the model (with borrowed strength from nonparametric Bayesian statistics) and interesting applications.

【邀请人】 冯兴东