Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey

This paper is a survey of estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and so-called simple estimating...

Full description

Saved in:
Bibliographic Details
Published in:International statistical review 2004-12, Vol.72 (3), p.337-354
Main Author: Sørensen, Helle
Format: Article
Language:English
Subjects:
Analytical estimating
Applications
Approximation
Bayesian analysis
Diffusion processes
Discrete-time observations
Efficient method of moments (EMM)
Estimating functions
Estimation methods
Estimators
Exact sciences and technology
Indirect inference
Inference
Likelihood approximations
Markov processes
Martingales
Mathematics
Maximum likelihood estimation
Maximum likelihood estimators
Modeling
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic models
Stochastic processes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is a survey of estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and so-called simple estimating functions; (ii) analytical and numerical approximations of the likelihood function which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation. /// Cet article propose un tour d'horizon de techniques d'estimation pour des processus de diffusion stationnaires et ergodiques observés à des moments discrets. On y présente les techniques suivantes: (i) fonctions d'estimation, l'accent étant mis sur des fonctions faisant intervenir une martingale et sur des fonctions d'estimation dites simples; (ii) approximations analytiques et numériques de la fonction de vraisemblance admettant, en principe, une précision arbitraire; (iii) analyse bayesienne et méthodes MCMC; (iv) inférence indirecte et méthode EMM, toutes deux introduisant des modèles auxiliaires (mais incorrects) et rectifiant, par simulation, le biais résultant.
ISSN:0306-7734
1751-5823
DOI:10.1111/j.1751-5823.2004.tb00241.x