Statistical Inference for Discretely Observed Markov Jump Processes
- 24 May 2005
- journal article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 67 (3) , 395-410
- https://doi.org/10.1111/j.1467-9868.2005.00508.x
Abstract
Summary: Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Markov chain Monte Carlo procedure. When the maximum likelihood estimator does not exist, an estimator can be obtained by using a penalized likelihood function or by the Markov chain Monte Carlo procedure with a suitable prior. The methodology and its implementation are illustrated by examples and simulation studies.Keywords
Funding Information
- Centre for Mathematical Physics
- Danish National Research Foundation
- European Community's ‘Human potential programme’ (HPRN-CT-2000-00100)
- Danish Social Science Research Council
This publication has 19 references indexed in Scilit:
- Direct Calculation of the Information Matrix via the EM AlgorithmJournal of the Royal Statistical Society Series B: Statistical Methodology, 1999
- L p Estimation of the Diffusion CoefficientBernoulli, 1999
- Estimating Equations Based on Eigenfunctions for a Discretely Observed Diffusion ProcessBernoulli, 1999
- On the Convergence Properties of the EM AlgorithmThe Annals of Statistics, 1983
- Maximum Likelihood Estimation in the Birth-and-Death ProcessThe Annals of Statistics, 1975
- Some Results on the Imbedding Problem for Finite Markov ChainsJournal of the London Mathematical Society, 1974
- Estimation in the birth processBiometrika, 1974
- The Logarithm Function for Finite-State Markov Semi-GroupsJournal of the London Mathematical Society, 1973
- On Uniqueness of the Logarithm for Markov Semi-GroupsJournal of the London Mathematical Society, 1972
- On the existence and uniqueness of the real logarithm of a matrixProceedings of the American Mathematical Society, 1966