{"paper":{"title":"Central limit theorem for a partially observed interacting system of Hawkes processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Chenguang Liu","submitted_at":"2019-06-19T13:01:32Z","abstract_excerpt":"We observe the actions of a $K$ sub-sample of $N$ individuals up to time $t$ for some large $K\\le N$. We model the relationships of individuals by i.i.d. Bernoulli($p$)-random variables, where $p\\in (0,1]$ is an unknown parameter. The rate of action of each individual depends on some unknown parameter $\\mu> 0$ and on the sum of some function $\\phi$ of the ages of the actions of the individuals which influence him. The parameters $\\mu$ and $\\phi$ 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 \\cite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08080","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}