Non-parametric estimation of the diffusion coefficient from noisy data - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2012

Non-parametric estimation of the diffusion coefficient from noisy data

Emeline Schmisser
  • Fonction : Auteur
  • PersonId : 857737

Résumé

Abstract We consider a diffusion process \left(X_{t}\right)_{t\geq0}, with drift b(x) and diffusion coefficient \sigma(x). At discrete times t_{k}=k\delta for k from 1 to M, we observe noisy data of the sample path, Y_{k\delta}=X_{k\delta}+\varepsilon_{k}. The random variables \left(\varepsilon_{k}\right) are i.i.d, centred and independent of \left(X_{t}\right). The process \left(X_{t}\right)_{t\geq0} is assumed to be strictly stationary, \beta-mixing and ergodic. In order to reduce the noise effect, we split data into groups of equal size p and build empirical means. The group size p is chosen such that \Delta=p\delta is small whereas M\delta is large. Then, the diffusion coefficient \sigma^{2} is estimated in a compact set A in a non-parametric way by a penalized least squares approach and the risk of the resulting adaptive estimator is bounded. We provide several examples of diffusions satisfying our assumptions and we carry out various simulations. Our simulation results illustrate the theoretical properties of our estimators.
Fichier principal
Vignette du fichier
estimation_sigma_bruit_ang.pdf (477.37 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00443993 , version 1 (05-01-2010)

Identifiants

Citer

Emeline Schmisser. Non-parametric estimation of the diffusion coefficient from noisy data. Statistical Inference for Stochastic Processes, 2012, 15 (3), pp 193-223. ⟨10.1007/s11203-012-9072-8⟩. ⟨hal-00443993⟩
170 Consultations
603 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More