IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v139y2018icp141-151.html
   My bibliography  Save this article

On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion

Author

Listed:
  • Kordzakhia, Nino E.
  • Kutoyants, Yury A.
  • Novikov, Alexander A.
  • Hin, Lin-Yee

Abstract

We provide new results concerning the limit distributions of Bayesian estimators (BE) and maximum likelihood estimators (MLE) of location parameters of cusp-type signals in “signal plus white noise” models. The limit distributions of BE and MLE are expressed in terms of fractional Brownian motion (fBm) with the Hurst parameter H, 0

Suggested Citation

  • Kordzakhia, Nino E. & Kutoyants, Yury A. & Novikov, Alexander A. & Hin, Lin-Yee, 2018. "On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 141-151.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:141-151
    DOI: 10.1016/j.spl.2018.04.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218301445
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.04.004?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. Fujii, Takayuki, 2010. "An extension of cusp estimation problem in ergodic diffusion processes," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 779-783, May.
    2. Pflug, Georg, 1982. "A statistically important Gaussian Process," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 45-57, July.
    3. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2018. "On parameter estimation for cusp-type signals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 39-62, February.
    4. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
    5. Alexander Gushchin & Uwe Küchler, 2011. "On estimation of delay location," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 273-305, October.
    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. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: cusp case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1137-1157, October.

    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. S. Dachian & N. Kordzakhia & Yu. A. Kutoyants & A. Novikov, 2018. "Estimation of cusp location of stochastic processes: a survey," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 345-362, July.
    2. Fujii Takayuki, 2009. "Cusp estimation in random design regression models," Statistics & Risk Modeling, De Gruyter, vol. 27(3), pages 235-248, December.
    3. Alexander Gushchin & Uwe Küchler, 2011. "On estimation of delay location," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 273-305, October.
    4. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2018. "On parameter estimation for cusp-type signals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 39-62, February.
    5. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: cusp case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1137-1157, October.
    6. O. V. Chernoyarov & Yu. A. Kutoyants, 2020. "Poisson source localization on the plane: the smooth case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 411-435, May.
    7. Yury A. Kutoyants, 2017. "The asymptotics of misspecified MLEs for some stochastic processes: a survey," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 347-367, October.
    8. C. Farinetto & Yu. A. Kutoyants & A. Top, 2020. "Poisson source localization on the plane: change-point case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 675-698, June.
    9. Arij Amiri & Sergueï Dachian, 2021. "On smooth change-point location estimation for Poisson Processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 499-524, October.
    10. Sergueï Dachian & Lin Yang, 2015. "On a Poissonian change-point model with variable jump size," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 127-150, July.

    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:eee:stapro:v:139:y:2018:i:c:p:141-151. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.