Central limit theorem for a partially observed interacting system of Hawkes processes

2019/06/19 by Liu, Chenguang
#60J75 #60K35 #62M09 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1906.08080

Abstract

We observe the actions of a K sub-sample of N individuals up to time t for some large K≤ N. We model the relationships of individuals by i.i.d. Bernoulli(p)-random variables, where p∈ (0,1] is an unknown parameter. The rate of action of each individual depends on some unknown parameter μ> 0 and on the sum of some function ϕ of the ages of the actions of the individuals which influence him. The parameters μ and ϕ are considered as nuisance parameters. The aim of this paper is to obtain a central limit theorem for the estimator of p that we introduced in \citeD, both in the subcritical and supercritical cases.

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