Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

Antoine Lejay 1, 2
1 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We study the asymptotic property of simple estimator of the parameter of a Skew Brownian Motion when one observes its positions on a fixed grid — or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the Maximum Likelihood Estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and is asymptotically mixed normal. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the Skew Brownian Motion observed at discrete times which is studied in a companion paper.
Type de document :
Article dans une revue
Statistical Inference for Stochastic Processes, Springer Verlag, 2017, 〈10.1007/s11203-017-9161-9〉
Liste complète des métadonnées

https://hal.inria.fr/hal-01319319
Contributeur : Antoine Lejay <>
Soumis le : vendredi 12 mai 2017 - 16:29:00
Dernière modification le : samedi 27 janvier 2018 - 01:31:49

Fichier

srw_estimation_hal.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Relations

Citation

Antoine Lejay. Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion. Statistical Inference for Stochastic Processes, Springer Verlag, 2017, 〈10.1007/s11203-017-9161-9〉. 〈hal-01319319v4〉

Partager

Métriques

Consultations de la notice

291

Téléchargements de fichiers

105