IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v83y2021i2d10.1007_s13171-020-00230-3.html
   My bibliography  Save this article

Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects

Author

Listed:
  • B. L. S. Prakasa Rao

    (CR RAO Advanced Institute of Mathematics, Statistics and Computer Science)

Abstract

We discuss nonparametric estimation of the density of random effects in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:2:d:10.1007_s13171-020-00230-3
    DOI: 10.1007/s13171-020-00230-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-020-00230-3
    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/s13171-020-00230-3?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. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    2. 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.
    3. Antic, J. & Laffont, C.M. & Chafaï, D. & Concordet, D., 2009. "Comparison of nonparametric methods in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 642-656, January.
    4. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    5. 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.
    6. 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)

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Nualart, David & Pérez-Abreu, Victor, 2014. "On the eigenvalue process of a matrix fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4266-4282.
    8. 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).
    9. Dai, Min & Duan, Jinqiao & Liao, Junjun & Wang, Xiangjun, 2021. "Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    10. 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.
    11. Lihong Guo, 2024. "Renormalization Group Method for a Stochastic Differential Equation with Multiplicative Fractional White Noise," Mathematics, MDPI, vol. 12(3), pages 1-20, January.
    12. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    13. John-Fritz Thony & Jean Vaillant, 2022. "Parameter Estimation for a Fractional Black–Scholes Model with Jumps from Discrete Time Observations," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    14. Čoupek, P. & Maslowski, B., 2017. "Stochastic evolution equations with Volterra noise," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 877-900.
    15. Falkowski, Adrian & Słomiński, Leszek, 2017. "SDEs with constraints driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3536-3557.
    16. Kęstutis Kubilius & Aidas Medžiūnas, 2020. "Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient," Mathematics, MDPI, vol. 9(1), pages 1-14, December.
    17. Marc Mukendi Mpanda & Safari Mukeru & Mmboniseni Mulaudzi, 2020. "Generalisation of Fractional-Cox-Ingersoll-Ross Process," Papers 2008.07798, arXiv.org, revised Jul 2022.
    18. Pavel Kříž & Leszek Szała, 2020. "Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    19. Zhang, Yinghan & Yang, Xiaoyuan, 2015. "Fractional stochastic Volterra equation perturbed by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 20-36.
    20. Hong, Jialin & Huang, Chuying & Kamrani, Minoo & Wang, Xu, 2020. "Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2675-2692.

    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:sankha:v:83:y:2021:i:2:d:10.1007_s13171-020-00230-3. 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.