IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v79y2016i8d10.1007_s00184-016-0583-y.html
   My bibliography  Save this article

Nonparametric estimation in a mixed-effect Ornstein–Uhlenbeck model

Author

Listed:
  • Charlotte Dion

    (Université Grenoble Alpes
    Université Paris Descartes)

Abstract

Two adaptive nonparametric procedures are proposed to estimate the density of the random effects in a mixed-effect Ornstein–Uhlenbeck model. First a kernel estimator is introduced with a new bandwidth selection method developed recently by Goldenshluger and Lepski (Ann Stat 39:1608–1632, 2011). Then, we adapt an estimator from Comte et al. (Stoch Process Appl 7:2522–2551, 2013) in the framework of small time interval of observation. More precisely, we propose an estimator that uses deconvolution tools and depends on two tuning parameters to be chosen in a data-driven way. The selection of these two parameters is achieved through a two-dimensional penalized criterion. For both adaptive estimators, risk bounds are provided in terms of integrated $$\mathbb {L}^2$$ L 2 -error. The estimators are evaluated on simulations and show good results. Finally, these nonparametric estimators are applied to neuronal data and are compared with previous parametric estimations.

Suggested Citation

  • Charlotte Dion, 2016. "Nonparametric estimation in a mixed-effect Ornstein–Uhlenbeck model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 919-951, November.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:8:d:10.1007_s00184-016-0583-y
    DOI: 10.1007/s00184-016-0583-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-016-0583-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-016-0583-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/1124 is not listed on IDEAS
    2. Lacour, C. & Massart, P., 2016. "Minimal penalty for Goldenshluger–Lepski method," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3774-3789.
    3. Hoffmann, Marc, 1999. "Adaptive estimation in diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 135-163, January.
    4. 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.
    5. Comte, Fabienne & Johannes, Jan, 2012. "Adaptive functional linear regression," LIDAM Reprints ISBA 2012031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. repec:dau:papers:123456789/4642 is not listed on IDEAS
    7. 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.
    8. repec:dau:papers:123456789/11429 is not listed on IDEAS
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maud Delattre & Valentine Genon-Catalot & Catherine Larédo, 2018. "Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 953-983, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    3. Wiqvist, Samuel & Golightly, Andrew & McLean, Ashleigh T. & Picchini, Umberto, 2021. "Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    4. B. L. S. Prakasa Rao, 2021. "Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 554-568, August.
    5. Mohammadi, Neda & Santoro, Leonardo V. & Panaretos, Victor M., 2024. "Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    6. 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.
    7. 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.
    8. 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.
    9. Maud Delattre & Valentine Genon-Catalot & Catherine Larédo, 2018. "Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 953-983, November.
    10. 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.
    11. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    12. Nicolas Asin & Jan Johannes, 2017. "Adaptive nonparametric estimation in the presence of dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 694-730, October.
    13. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    14. Aït-Sahalia, Yacine & Park, Joon Y., 2016. "Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models," Journal of Econometrics, Elsevier, vol. 192(1), pages 119-138.
    15. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.
    16. Hoffmann, Marc & Marguet, Aline, 2019. "Statistical estimation in a randomly structured branching population," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5236-5277.
    17. Wooyong Lee & Priscilla E. Greenwood & Nancy Heckman & Wolfgang Wefelmeyer, 2017. "Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 237-252, July.
    18. Park, Joon Y. & Wang, Bin, 2021. "Nonparametric estimation of jump diffusion models," Journal of Econometrics, Elsevier, vol. 222(1), pages 688-715.
    19. Heinz Schmidli & Beat Neuenschwander, 2012. "Discussions," Biometrics, The International Biometric Society, vol. 68(1), pages 212-214, March.
    20. Schmisser Emeline, 2011. "Non-parametric drift estimation for diffusions from noisy data," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 119-150, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:79:y:2016:i:8:d:10.1007_s00184-016-0583-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.