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In this work, we study the event occurrences of user activities on online social network platforms. To characterize the social activity interactions among network users, we propose a network group Hawkes (NGH) process model. Particularly, the observed network structure information is employed to model the users dynamic posting behaviors. Furthermore, the users are clustered into latent groups according to their dynamic behavior patterns. To estimate the model, a constraint maximum likelihood approach is proposed. Theoretically, we establish the consistency and asymptotic normality of the estimators. In addition, we show that the group memberships can be identified consistently. To conduct estimation, a branching representation structure is firstly introduced, and a stochastic EM (StEM) algorithm is developed to tackle the computational problem. Lastly, we apply the proposed method to a social network data collected from Sina Weibo, and identify the infuential network users as an interesting application.
We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent $beta + 1 in (1,2]$, this replacement has the advantage that the Laplace trans
We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling.
The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal cont
Change-points are a routine feature of big data observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small number of a
This paper deals with the optimization of industrial asset management strategies, whose profitability is characterized by the Net Present Value (NPV) indicator which is assessed by a Monte Carlo simulator. The developed method consists in building a