Séminaire Jeunes chercheurs (Maël Duverger, jeudi 31 octobre 2024)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 31 octobre 2024 à 17h en salle A707. Nous aurons le plaisir d'écouter Maël Duverger (CEREMADE), qui nous parlera de

Bernstein-von Mises property for functionals of linear Hawkes processes.

Abstract
Hawkes processes are point processes used to model self-exciting phenomena. In the linear multivariate case, where the number of components K is fixed, the Hawkes process is defined by a set of parameters composed of K positive real numbers and K^2 non negative functions (called excitation functions). There have been some recent results on Bayesian estimation of these parameters, in particular concentration rates for the posterior distribution have been obtained by Donnet et al. (2020) and Sulem et al. (2024). In this ongoing work, based on these recent results, we aim to derive a Bernstein-von Mises property for some smooth functionals of the parameters. Broadly speaking, Bernstein-von Mises property states that the posterior distribution behaves asymptotically as a gaussian distribution, centered at an efficient estimator. Castillo and Rousseau proved in 2015 a general theorem for obtaining such a property in semiparametric models, which we intend to apply in this Hawkes processes framework.