Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313485793> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W4313485793 abstract "We consider a population of $N$ individuals, of which we observe the number of actions as time evolves. For each couple of individuals $(i,j)$, $j$ may or not influence $i$, which we model by i.i.d. Bernoulli$(p)$-random variables, for some unknown parameter $pin (0,1]$. Each individual acts autonomously at some unknown rate $mu>0$ and acts by mimetism at some rate depending on the number of recent actions of the individuals which influence him, the age of these actions being taken into account through an unknown function $varphi$ (roughly, decreasing and with fast decay). The goal of this paper is to estimate $p$, which is the main charateristic of the graph of interactions, in the asymptotic $Ntoinfty$, $ttoinfty$. The main issue is that the mean field limit (as $N to infty$) of this model is unidentifiable, in that it only depends on the parameters $mu$ and $pvarphi$. Fortunately, this mean field limit is not valid for large times. We distinguish the subcritical case, where, roughly, the mean number $m_t$ of actions per individual increases linearly and the supercritical case, where $m_t$ increases exponentially. Although the nuisance parameter $varphi$ is non-parametric, we are able, in both cases, to estimate $p$ without estimating $varphi$ in a nonparametric way, with a precision of order $N^{-1/2}+N^{1/2}m_t^{-1}$, up to some arbitrarily small loss. We explain, using a Gaussian toy model, the reason why this rate of convergence might be (almost) optimal." @default.
- W4313485793 created "2023-01-06" @default.
- W4313485793 creator A5051974030 @default.
- W4313485793 creator A5065420785 @default.
- W4313485793 date "2015-07-10" @default.
- W4313485793 modified "2023-10-14" @default.
- W4313485793 title "Statistical inference versus mean field limit for Hawkes processes" @default.
- W4313485793 doi "https://doi.org/10.48550/arxiv.1507.02887" @default.
- W4313485793 hasPublicationYear "2015" @default.
- W4313485793 type Work @default.
- W4313485793 citedByCount "0" @default.
- W4313485793 crossrefType "posted-content" @default.
- W4313485793 hasAuthorship W4313485793A5051974030 @default.
- W4313485793 hasAuthorship W4313485793A5065420785 @default.
- W4313485793 hasBestOaLocation W43134857931 @default.
- W4313485793 hasConcept C102366305 @default.
- W4313485793 hasConcept C105795698 @default.
- W4313485793 hasConcept C114614502 @default.
- W4313485793 hasConcept C121332964 @default.
- W4313485793 hasConcept C134306372 @default.
- W4313485793 hasConcept C144024400 @default.
- W4313485793 hasConcept C149923435 @default.
- W4313485793 hasConcept C151201525 @default.
- W4313485793 hasConcept C15964574 @default.
- W4313485793 hasConcept C163716315 @default.
- W4313485793 hasConcept C166785042 @default.
- W4313485793 hasConcept C185429906 @default.
- W4313485793 hasConcept C19448537 @default.
- W4313485793 hasConcept C194531419 @default.
- W4313485793 hasConcept C202213908 @default.
- W4313485793 hasConcept C2908647359 @default.
- W4313485793 hasConcept C33923547 @default.
- W4313485793 hasConcept C62520636 @default.
- W4313485793 hasConcept C75438885 @default.
- W4313485793 hasConceptScore W4313485793C102366305 @default.
- W4313485793 hasConceptScore W4313485793C105795698 @default.
- W4313485793 hasConceptScore W4313485793C114614502 @default.
- W4313485793 hasConceptScore W4313485793C121332964 @default.
- W4313485793 hasConceptScore W4313485793C134306372 @default.
- W4313485793 hasConceptScore W4313485793C144024400 @default.
- W4313485793 hasConceptScore W4313485793C149923435 @default.
- W4313485793 hasConceptScore W4313485793C151201525 @default.
- W4313485793 hasConceptScore W4313485793C15964574 @default.
- W4313485793 hasConceptScore W4313485793C163716315 @default.
- W4313485793 hasConceptScore W4313485793C166785042 @default.
- W4313485793 hasConceptScore W4313485793C185429906 @default.
- W4313485793 hasConceptScore W4313485793C19448537 @default.
- W4313485793 hasConceptScore W4313485793C194531419 @default.
- W4313485793 hasConceptScore W4313485793C202213908 @default.
- W4313485793 hasConceptScore W4313485793C2908647359 @default.
- W4313485793 hasConceptScore W4313485793C33923547 @default.
- W4313485793 hasConceptScore W4313485793C62520636 @default.
- W4313485793 hasConceptScore W4313485793C75438885 @default.
- W4313485793 hasLocation W43134857931 @default.
- W4313485793 hasLocation W43134857932 @default.
- W4313485793 hasOpenAccess W4313485793 @default.
- W4313485793 hasPrimaryLocation W43134857931 @default.
- W4313485793 hasRelatedWork W2082786936 @default.
- W4313485793 hasRelatedWork W2091650952 @default.
- W4313485793 hasRelatedWork W2118216969 @default.
- W4313485793 hasRelatedWork W2436187474 @default.
- W4313485793 hasRelatedWork W2769873724 @default.
- W4313485793 hasRelatedWork W2952793926 @default.
- W4313485793 hasRelatedWork W4298083760 @default.
- W4313485793 hasRelatedWork W4299418272 @default.
- W4313485793 hasRelatedWork W4307626464 @default.
- W4313485793 hasRelatedWork W1950412443 @default.
- W4313485793 isParatext "false" @default.
- W4313485793 isRetracted "false" @default.
- W4313485793 workType "article" @default.