Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion

Maud Delattre (), Valentine Genon-Catalot () and Catherine Larédo ()
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Maud Delattre: Université Paris-Saclay
Valentine Genon-Catalot: UMR CNRS 8145, Laboratoire MAP5, Université Paris Descartes, Sorbonne Paris Cité
Catherine Larédo: INRA, MaIAGE

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 8, No 3, 953-983

Abstract: Abstract Consider N independent stochastic processes $$(X_i(t), t\in [0,T])$$ ( X i ( t ) , t ∈ [ 0 , T ] ) , $$i=1,\ldots , N$$ i = 1 , … , N , defined by a stochastic differential equation with random effects where the drift term depends linearly on a random vector $$\Phi _i$$ Φ i and the diffusion coefficient depends on another linear random effect $$\Psi _i$$ Ψ i . For these effects, we consider a joint parametric distribution. We propose and study two approximate likelihoods for estimating the parameters of this joint distribution based on discrete observations of the processes on a fixed time interval. Consistent and $$\sqrt{N}$$ N -asymptotically Gaussian estimators are obtained when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated data and show good performances.

Keywords: Asymptotic properties; Discrete observations; Estimating equations; Parametric inference; Random effects models; Stochastic differential equations (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-018-0666-z

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