IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i14p2066-2074.html
   My bibliography  Save this article

On weak convergence of the likelihood ratio process in multi-phase regression models

Author

Listed:
  • Fujii, Takayuki

Abstract

The purpose of this paper is to study the change point estimation problem in multi-phase regression models. This is a non-regular statistical estimation; thus the asymptotic distribution of the maximum likelihood estimator is verified by means of the weak convergence of the likelihood ratio process. These weak convergence results differ depending on the jump size of the regression function.

Suggested Citation

  • Fujii, Takayuki, 2008. "On weak convergence of the likelihood ratio process in multi-phase regression models," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2066-2074, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2066-2074
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00079-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gut, Allan & Janson, Svante, 2001. "Tightness and weak convergence for jump processes," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 101-107, March.
    2. Ciuperca Gabriela, 2004. "Maximum likelihood estimator in a two-phase nonlinear random regression model," Statistics & Risk Modeling, De Gruyter, vol. 22(4/2004), pages 335-349, April.
    3. Fujii, Takayuki, 2007. "A note on the asymptotic distribution of the maximum likelihood estimator in a non-regular case," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1622-1627, October.
    4. Koul, Hira L. & Qian, Lianfen & Surgailis, Donatas, 2003. "Asymptotics of M-estimators in two-phase linear regression models," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 123-154, January.
    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. 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.

    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. Sergueï Dachian & Ilia Negri, 2011. "On compound Poisson processes arising in change-point type statistical models as limiting likelihood ratios," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 255-271, October.
    2. Ciuperca, Gabriela, 2009. "The M-estimation in a multi-phase random nonlinear model," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 573-580, March.
    3. Zhang, Li-Xin & Chan, Wai-Sum & Cheung, Siu-Hung & Hung, King-Chi, 2009. "A note on the consistency of a robust estimator for threshold autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 807-813, March.
    4. Dupuy, Jean-François, 2006. "Estimation in a change-point hazard regression model," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 182-190, January.
    5. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2015. "Estimators in step regression models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 124-129.
    6. Ferger Dietmar & Klotsche Jens, 2009. "Estimation of split-points in binary regression," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 93-128, December.
    7. Fuxia Cheng & Hira L. Koul, 2023. "An analog of Bickel–Rosenblatt test for fitting an error density in the two phase linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 27-56, January.
    8. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.
    9. Gill, Ryan & Lee, Kiseop & Song, Seongjoo, 2007. "Computation of estimates in segmented regression and a liquidity effect model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6459-6475, August.
    10. Bryc, Wlodzimierz & Wesolowski, Jacek, 2006. "The classical bi-Poisson process: An invertible quadratic harness," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1664-1674, September.
    11. Gabriela Ciuperca, 2011. "Penalized least absolute deviations estimation for nonlinear model with change-points," Statistical Papers, Springer, vol. 52(2), pages 371-390, May.
    12. Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.
    13. 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.
    14. Chung-Ming Kuan & Christos Michalopoulos & Zhijie Xiao, 2017. "Quantile Regression on Quantile Ranges – A Threshold Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 99-119, January.
    15. Yury Kutoyants, 2012. "On identification of the threshold diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 383-413, April.

    More about this item

    Statistics

    Access and download statistics

    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:78:y:2008:i:14:p:2066-2074. 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.