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Parametric inference for discrete observations of diffusion processes with mixed effects

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  • Delattre, Maud
  • Genon-Catalot, Valentine
  • Larédo, Catherine

Abstract

Stochastic differential equations with mixed effects provide means to model intra-individual and inter-individual variability in repeated experiments leading to longitudinal data. We consider N i.i.d. stochastic processes defined by a stochastic differential equation with linear mixed effects which are discretely observed. We study a parametric framework with distributions leading to explicit approximate likelihood functions and investigate the asymptotic behavior of estimators under the asymptotic framework : the number N of individuals (trajectories) and the number n of observations per individual tend to infinity within a fixed time interval. The estimation method is assessed on simulated data for various models.

Suggested Citation

  • Delattre, Maud & Genon-Catalot, Valentine & Larédo, Catherine, 2018. "Parametric inference for discrete observations of diffusion processes with mixed effects," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1929-1957.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:6:p:1929-1957
    DOI: 10.1016/j.spa.2017.08.016
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/1124 is not listed on IDEAS
    2. Comte, F. & Genon-Catalot, V. & Samson, A., 2013. "Nonparametric estimation for stochastic differential equations with random effects," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2522-2551.
    3. repec:dau:papers:123456789/4642 is not listed on IDEAS
    4. Umberto Picchini & Andrea De Gaetano & Susanne Ditlevsen, 2010. "Stochastic Differential Mixed‐Effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 67-90, March.
    5. L. Nie, 2006. "Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear and Nonlinear Mixed-Effects Models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 123-143, April.
    6. Maud Delattre & Valentine Genon-Catalot & Adeline Samson, 2013. "Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 322-343, June.
    7. Picchini, Umberto & Ditlevsen, Susanne, 2011. "Practical estimation of high dimensional stochastic differential mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1426-1444, March.
    8. Sophie Donnet & Jean-Louis Foulley & Adeline Samson, 2010. "Bayesian Analysis of Growth Curves Using Mixed Models Defined by Stochastic Differential Equations," Biometrics, The International Biometric Society, vol. 66(3), pages 733-741, September.
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    Cited by:

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    2. Nicolas Marie, 2023. "Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models," Finance and Stochastics, Springer, vol. 27(1), pages 97-126, January.
    3. Fabienne Comte & Nicolas Marie, 2021. "Nonparametric estimation for I.I.D. paths of fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 669-705, October.

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