Nonparametric adaptive estimation for interacting particle systems - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

Nonparametric adaptive estimation for interacting particle systems

Fabienne Comte
Valentine Genon-Catalot
  • Fonction : Auteur
  • PersonId : 1037577

Résumé

We consider a stochastic system (X N i (t), i = 1,. .. , N) of N interacting particles with constant diusion coecient and linear drift b(t, x, µ) = α(t)x − β(t) (x − y)µ(dy) depending on two unknown deterministic functions α(t), β(t). Our concern here is the nonparametric estimation of these functions from a continuous observation of the process on [0, T ] for xed T and large N. We dene two collections of projection estimators αm(t), γ p (t) respectively of α(t), γ(t) = α(t) − β(t) where for each m (resp. p), αm(t) (resp. γ p (t)) belongs to a nite dimensional subspace of L 2 ([0, T ]). We study the L 2-risks of these estimators where the risk is dened either by the expectation of an empirical norm or by the expectation of a deterministic norm. Afterwards, we propose a data-driven choice m (resp. p) of the value m (resp. p) and study the risk of the adaptive estimators. The case of β(t) ≡ 0 is also treated separately. The results are illustrated by numerical experiments on simulated data.
Fichier principal
Vignette du fichier
FinalInteractingSJS.pdf (886.44 Ko) Télécharger le fichier
FinalInteractingSJS (1).pdf (886.44 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03696877 , version 1 (16-06-2022)
hal-03696877 , version 2 (09-05-2023)

Identifiants

  • HAL Id : hal-03696877 , version 2

Citer

Fabienne Comte, Valentine Genon-Catalot. Nonparametric adaptive estimation for interacting particle systems. 2022. ⟨hal-03696877v2⟩
61 Consultations
157 Téléchargements

Partager

More