ArticleOriginal scientific text
Title
Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion
Authors 1
Affiliations
- Department of Mathematics, New University of Lisbon, Portugal
Abstract
When a diffusion is ergodic its transition density converges to its invariant density, see Durrett (1998). This convergence enabled us to introduce a sample partitioning technique that gives in each sub-sample, maximum likelihood estimators. The averages of these being a natural choice as estimators. To compare our estimators with the optimal we obtained from martingale estimating functions, see Sørensen (1998), we used the Ornstein-Uhlenbeck process for which exact simulations can be carried out.
Keywords
ergodic diffusions, martingale estimating functions, transition and invariant densities, maximum likelihood estimators
Bibliography
- B.M. Bibby and M. Sørensen, Martingale estimation functions for discretely observed diffusion processes, Bernoulli 1 (1995), 17-39.
- U. Küchler and M. Sørensen, Exponential Families of Stochastic Processes, Springer-Verlag 1997.
- S. Iacus, Simulation and Inference for Stochastic Differential, Equations with R Examples, Springer 2008.
- J.T. Mexia and G.C. Dias, Statistical Inference for Discretely Observed Diffusions of Diffusions, VII-Congresso da SPE, 14-16 Outubro, Osir 1999.
- B. Øksendal, Stochastic Differential Equations, An Introduction, Fifth Edition, Springer-Verlag 1998.
- M. Sørensen, Lecture Notes on 'Statistical Inference for Discretely Observed Diffusions', Berlin Graduiertenkolleg 1998.
Pages:
117-122
Main language of publication
English
Received
2010-01-18
Published
2010
DOI: 10.7151/dmps.1124
Exact and natural sciences