Maximum likelihood estimation for stochastic differential equations with random effects

Abstract : We consider $N$ independent stochastic processes $(X_i(t), t\in [0,T_i])$, $i=1,\ldots, N$, defined by a stochastic differential equation with drift term depending on a random variable $\phi_i$. The distribution of the random effect $\phi_i$ depends on unknown parameters which are to be estimated from the continuous observation of the processes $X_i$. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect $\phi_i$ and $\phi_i$ has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when $T_i=T$ for all $i$ and $N$ tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large.
Complete list of metadatas

Cited literature [9 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00650844
Contributor : Adeline Samson <>
Submitted on : Monday, December 12, 2011 - 1:26:13 PM
Last modification on : Monday, December 23, 2019 - 3:50:10 PM
Long-term archiving on: Friday, November 16, 2012 - 3:12:35 PM

File

submission_delattre_etal.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Maud Delattre, Valentine Genon-Catalot, Adeline Samson. Maximum likelihood estimation for stochastic differential equations with random effects. Scandinavian Journal of Statistics, Wiley, 2013, 40 (2), pp.322-343. ⟨10.1111/j.1467-9469.2012.00813.x/abstract⟩. ⟨hal-00650844⟩

Share

Metrics

Record views

422

Files downloads

459