IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v70y2018i1d10.1007_s10463-016-0581-x.html
   My bibliography  Save this article

On parameter estimation for cusp-type signals

Author

Listed:
  • O. V. Chernoyarov

    (National Research University “MPEI”)

  • S. Dachian

    (National Research University “MPEI”
    Laboratoire Paul Painlevé, UMR CNRS 8524, Cité Scientifique)

  • Yu. A. Kutoyants

    (National Research University “MPEI”
    Université du Maine)

Abstract

We consider the problem of parameter estimation by continuous time observations of a deterministic signal in white Gaussian noise. It is supposed that the signal has a cusp-type singularity. The properties of the maximum-likelihood and Bayesian estimators are described in the asymptotics of small noise. Special attention is paid to the problem of parameter estimation in the situation of misspecification in regularity, i.e., when the statistician supposes that the observed signal has this singularity, but the real signal is smooth. The rate and the asymptotic distribution of the maximum-likelihood estimator in this situation are described.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-016-0581-x
    DOI: 10.1007/s10463-016-0581-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-016-0581-x
    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/s10463-016-0581-x?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. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
    2. Maik Döring & Uwe Jensen, 2015. "Smooth change point estimation in regression models with random design," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 595-619, June.
    3. Prakasa Rao, B. L. S., 2004. "Estimation of cusp in nonregular nonlinear regression models," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 243-251, February.
    4. 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.
    5. Rao, B. L. S. Prakasa, 1985. "Asymptotic theory of least squares estimator in a nonregular nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 3(1), pages 15-18, February.
    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. 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. 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.
    3. 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. 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.
    4. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    5. Alexander Gushchin & Uwe Küchler, 2011. "On estimation of delay location," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 273-305, 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. Prakasa Rao, B. L. S., 2004. "Estimation of cusp in nonregular nonlinear regression models," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 243-251, February.
    8. Maria Mohr & Leonie Selk, 2020. "Estimating change points in nonparametric time series regression models," Statistical Papers, Springer, vol. 61(4), pages 1437-1463, August.
    9. 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.
    10. Zhao, Wenbiao & Zhu, Lixing, 2024. "Detecting change structures of nonparametric regressions," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    11. 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.
    12. Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 135-144.
    13. 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.
    14. 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.
    15. Marie Hušková & Zuzana Prášková & Josef G. Steinebach, 2022. "Estimating a gradual parameter change in an AR(1)-process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 771-808, October.
    16. 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:spr:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-016-0581-x. 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.