IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v27y2009i3p235-248n1.html
   My bibliography  Save this article

Cusp estimation in random design regression models

Author

Listed:
  • Fujii Takayuki

Abstract

We consider the parametric estimation for the random design nonlinear regression model whose regression function has an unknown cusp location. The Fisher information of this location parameter is unbounded, that is caused by the non-differentiability of the likelihood function, so this is a non-regular estimation problem. In this paper, we verify the asymptotic properties of the Bayes estimator (BE), e.g. the consistency, the asymptotic distribution and the convergence of its moments, by the likelihood ratio process whose limit is expressed in terms of fractional Brownian motion. Further, we show that the BE is asymptotically efficient in a certain minimax sense.

Suggested Citation

  • Fujii Takayuki, 2009. "Cusp estimation in random design regression models," Statistics & Risk Modeling, De Gruyter, vol. 27(3), pages 235-248, December.
  • Handle: RePEc:bpj:strimo:v:27:y:2009:i:3:p:235-248:n:1
    DOI: 10.1524/stnd.2009.1035
    as

    Download full text from publisher

    File URL: https://doi.org/10.1524/stnd.2009.1035
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1524/stnd.2009.1035?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. 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.
    2. S. Dachian, 2003. "Estimation of Cusp Location by Poisson Observations," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 1-14, January.
    3. Pflug, Georg, 1982. "A statistically important Gaussian Process," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 45-57, July.
    4. 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)

    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. 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.
    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. 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.
    5. 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.
    6. 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.
    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. 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.
    10. 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.
    11. 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.
    12. 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:bpj:strimo:v:27:y:2009:i:3:p:235-248:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.