IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v79y2016i6d10.1007_s00184-015-0574-4.html
   My bibliography  Save this article

On multi-step MLE-process for Markov sequences

Author

Listed:
  • Yu. A. Kutoyants

    (Université du Maine
    National Research University “MPEI”)

  • A. Motrunich

    (Université du Maine
    Statésia)

Abstract

We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we estimate the unknown parameter by a learning relatively short part of observations and then we use the one-step MLE idea to construct an-estimator process which is asymptotically equivalent to the MLE. To have the learning interval shorter we introduce the two-step procedure which leads to the asymptotically efficient estimator-process too. The presented results are illustrated with the help of two numerical examples.

Suggested Citation

  • Yu. A. Kutoyants & A. Motrunich, 2016. "On multi-step MLE-process for Markov sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 705-724, August.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:6:d:10.1007_s00184-015-0574-4
    DOI: 10.1007/s00184-015-0574-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-015-0574-4
    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/s00184-015-0574-4?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. Yosihiko Ogata & Nobuo Inagaki, 1977. "The weak convergence of the likelihood ratio random fields for Markov observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 165-187, December.
    2. Kengo Kamatani & Masayuki Uchida, 2015. "Hybrid multi-step estimators for stochastic differential equations based on sampled data," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 177-204, July.
    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. Kutoyants, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
    2. Chamseddine Guizani & Mejdi Jeguirim & Sylvie Valin & Lionel Limousy & Sylvain Salvador, 2017. "Biomass Chars: The Effects of Pyrolysis Conditions on Their Morphology, Structure, Chemical Properties and Reactivity," Energies, MDPI, vol. 10(6), pages 1-18, June.
    3. Tawfik, M. & Tonnellier, X. & Sansom, C., 2018. "Light source selection for a solar simulator for thermal applications: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 90(C), pages 802-813.
    4. Wenqiang Sun & Yuhao Hong & Yanhui Wang, 2016. "Operation Optimization of Steam Accumulators as Thermal Energy Storage and Buffer Units," Energies, MDPI, vol. 10(1), pages 1-16, December.

    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. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.
    2. Masahiro Kurisaki, 2023. "Parameter estimation for ergodic linear SDEs from partial and discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 279-330, July.
    3. Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.
    4. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    5. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    6. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.
    7. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    8. Kutoyants, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
    9. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
    10. Tonaki, Yozo & Uchida, Masayuki, 2023. "Change point inference in ergodic diffusion processes based on high frequency data," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 1-39.
    11. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for stochastic differential equations from reduced data," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 435-454, July.
    12. Yusuke Kaino & Shogo H. Nakakita & Masayuki Uchida, 2020. "Hybrid estimation for ergodic diffusion processes based on noisy discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 171-198, April.
    13. Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.

    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:6:d:10.1007_s00184-015-0574-4. 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.