Bidimensional random effect estimation in mixed stochastic differential model

Dion, Charlotte; Genon-Catalot, Valentine

doi:10.1007/s11203-015-9122-0

Cited by 18 publications

(23 citation statements)

References 25 publications

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“…Our approach applies to general diffusion models and to general distributions for the random effects up to some moments constraints. The results obtained in Proposition 3.5 have been extended to the case of a multivariate random effect in the drift in Dion and Genon-Catalot (2015). It is then used to build nonparametric estimators of the joint density of the random effects.…”

Section: Discussionmentioning

confidence: 98%

Estimation for stochastic differential equations with mixed effects

Genon-Catalot

Larédo²

2016

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We consider the long term behaviour of a one-dimensional mixed effects diffusion process (X(t)) with a multivariate random effect φ in the drift coefficient. We first study the estimation of the random variable φ based on the observation of one sample path on the time interval [0, T ] as T tends to infinity. The process (X(t)) is not Markov and we characterize its invariant distributions. We build moments and maximum likelihood-type estimators of the random variable φ which are consistent and asymptotically mixed normal with rate √ T. Moreover, we obtain non asymptotic bounds for the moments of these estimators. Examples with a bivariate random effect are detailed. Afterwards, the estimation of parameters in the distribution of the random effect from N i.i.d. processes (Xj(t), t ∈ [0, T ]), j = 1,. .. , N is investigated. Estimators are built and studied as both N and T = T (N) tend to infinity. We prove that the convergence rate of estimators differs when deterministic components are present in the random effects. For true random effects, the rate of convergence is √ N whereas for deterministic components, the rate is √ N T. Illustrative examples are given.

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Section: Discussionmentioning

confidence: 98%

Estimation for stochastic differential equations with mixed effects

Genon-Catalot

Larédo²

2016

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“…Truncated versions of this estimator have been introduced for theoretical reasons. In the bidimensional case φ j = (α j , β j ), Dion and Genon-Catalot (2015) propose the following estimator…”

Section: Nonparametric Estimation Of the Random Effects Densitymentioning

confidence: 99%

“…The parametric approaches assume Gaussian random effects φ j . Among other references, for parametric maximum likelihood estimation, we can cite Ditlevsen and de Gaetano (2005); Picchini et al 2010 Three estimation procedures are implemented in the mixedsde package: a kernel nonparametric estimator (Dion and Genon-Catalot, 2015), a parametric maximum likelihood estimator (Delattre et al, 2013) and a parametric Bayesian estimator . The parametric frequentist and Bayesian approaches assume the random effects Gaussian.…”

Section: Introductionmentioning

confidence: 99%

mixedsde: A Package to Fit Mixed Stochastic Differential Equations

Dion¹,

Hermann²,

Samson³

2019

The R Journal

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Stochastic differential equations (SDEs) are useful to model continuous stochastic processes. When (independent) repeated temporal data are available, variability between the trajectories can be modeled by introducing random effects in the drift of the SDEs. These models are useful to analyze neuronal data, crack length data, pharmacokinetics, financial data, to cite some applications among other. The R package focuses on the estimation of SDEs with linear random effects in the drift. The goal is to estimate the common density of the random effects from repeated discrete observations of the SDE. The package mixedsde proposes three estimation methods: a Bayesian parametric, a frequentist parametric and a frequentist nonparametric method. The three procedures are described as well as the main functions of the package. Illustrations are presented on simulated and real data.

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“…This allows to build, when N trajectories are available, plug-in type parametric or nonparametric estimators of the random effects distributions (see e.g. Comte et al (2013), Dion and Genon-Catalot (2015), Genon-Catalot and Larédo (2015)). …”

Section: Introductionmentioning

confidence: 99%