Article (Scientific journals)
Contrast function estimation for the drift parameter of ergodic jump diffusion process
AMORINO, Chiara; Gloter, Arnaud
2020In Scandinavian Journal of Statistics
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Keywords :
Efficient drift estimation; ergodic properties; high frequency; Levy processes; thresholding methods; SDE with jumps
Abstract :
[en] In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter. We suppose that the process is discretely observed. We introduce an estimator based on a contrast function, which is efficient without requiring any conditions on the rate at which the step discretization goes to zero, and where we allow the observed process to have non summable jumps. This extends earlier results where the condition on the step discretization was needed and where the process was supposed to have summable jumps. In general situations, our contrast function is not explicit and one has to resort to some approximation. In the case of a finite jump activity, we propose explicit approximations of the contrast function, such that the efficient estimation of the drift parameter is feasible. This extends the results obtained by Kessler in the case of continuous processes.
Disciplines :
Mathematics
Author, co-author :
AMORINO, Chiara  ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Gloter, Arnaud ;  Université d'Evry > LaMMe
 These authors have contributed equally to this work.
External co-authors :
yes
Language :
English
Title :
Contrast function estimation for the drift parameter of ergodic jump diffusion process
Publication date :
2020
Journal title :
Scandinavian Journal of Statistics
ISSN :
1467-9469
Publisher :
Blackwell, Oxford, United Kingdom
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 24 November 2020

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