no. 5
Statistics
On likelihood estimation for a discretely observed jump process
[Sur l'estimation d'un processus de sauts discretisé]

Présenté par : Paul Deheuvels

Dehay, Dominique1 ; Yao, Jian-feng1
1 IRMAR, campus de Beaulieu, 35042 Rennes cedex, France
Comptes Rendus. Mathématique, Tome 342 (2006) no. 5, pp. 341-344.

Soit un processus de sauts markovien observé en des temps discrets. À l'aide d'une formule explicite de la vraisemblance de la chaîne observée, nous proposons une théorie asymptotique de l'estimateur de vraisemblance.

We consider the parameter estimation problem for a Markov jump process sampled at periodic epochs with a constant step. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, we provide here an explicit expression of the likelihood function of the sampled chain. Moreover under suitable ergodicity condition on the jump process, we establish the consistency and the asymptotic normality of the likelihood estimator as the observation period tends to infinity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.12.025
Dehay, Dominique 1 ; Yao, Jian-feng 1

1 IRMAR, campus de Beaulieu, 35042 Rennes cedex, France 
@article{CRMATH_2006__342_5_341_0,
     author = {Dehay, Dominique and Yao, Jian-feng},
     title = {On likelihood estimation for a discretely observed jump process},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {341--344},
     publisher = {Elsevier},
     volume = {342},
     number = {5},
     year = {2006},
     doi = {10.1016/j.crma.2005.12.025},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2005.12.025/}
}
TY  - JOUR
AU  - Dehay, Dominique
AU  - Yao, Jian-feng
TI  - On likelihood estimation for a discretely observed jump process
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 341
EP  - 344
VL  - 342
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2005.12.025/
DO  - 10.1016/j.crma.2005.12.025
LA  - en
ID  - CRMATH_2006__342_5_341_0
ER  - 
%0 Journal Article
%A Dehay, Dominique
%A Yao, Jian-feng
%T On likelihood estimation for a discretely observed jump process
%J Comptes Rendus. Mathématique
%D 2006
%P 341-344
%V 342
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2005.12.025/
%R 10.1016/j.crma.2005.12.025
%G en
%F CRMATH_2006__342_5_341_0
Dehay, Dominique; Yao, Jian-feng. On likelihood estimation for a discretely observed jump process. Comptes Rendus. Mathématique, Tome 342 (2006) no. 5, pp. 341-344. doi : 10.1016/j.crma.2005.12.025. http://www.numdam.org/articles/10.1016/j.crma.2005.12.025/

[1] Aït-Sahalia, Y. Maximum likelihood estimation for discretely sampled diffusions: a closed-form approximation approach, Econometrica, Volume 70 (2002), pp. 223-262

[2] Bladt, M.; Sørensen, M. Statistical inference for discretely observed Markov jump processes, J.R.S.S (B), Volume 67 (2005) no. 3, pp. 395-410

[3] B.M. Bibby, M. Jacobsen, M. Sørensen, Estimation functions for discretely sampled diffusion-type models, in: Y. Aït-Sahalia, L.P. Hansen (Eds.), Handbook of Financial Econometrics, North-Holland, Amsterdam, in press

[4] Billingsley, P. Statistical Inference for Markov Processes, The University of Chicago Press, Chicago, 1961

[5] Billingsley, P. Statistical methods in Markov chains, Ann. Math. Statist., Volume 32 (1961), pp. 12-40

[6] Dacunha-Castelle, D.; Duflo, M. Probability and Statistics, vol. II, Springer-Verlag, New York, 1986

[7] Keiding, N. Estimation in the birth process, Biometrika, Volume 61 (1974), pp. 71-80

[8] Keiding, N. Maximum likelihood estimation in the birth-and-death process, Ann. Statist., Volume 3 (1975), pp. 363-372

[9] Kessler, M.; Sørensen, M. Estimating equations based on eigenfunctions for discretely observed diffusion processes, Bernoulli, Volume 5 (1999), pp. 299-314

Cité par Sources :