IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v17y1984i2p337-347.html
   My bibliography  Save this article

Inference for earthquake models: A self-correcting model

Author

Listed:
  • Ogata, Y.
  • Vere-Jones, D.

Abstract

Questions of asymptotic inference are discussed for a point process model in which the conditional intensity function increases monotonically between events and drops by determined (nonrandom) amounts after each event. Parameter estimates are shown to be consistent and, except under the null hypothesis of a Poisson process, normally distributed. Under the null hypothesis, however, the Hessian matrix is not asymptotically constant, and the limiting distribution of the likelihood ratio statistics is not [chi]2, but has a form related to that of the Cramer-von Mises [omega]2 statistic for the test of goodness of fit.

Suggested Citation

  • Ogata, Y. & Vere-Jones, D., 1984. "Inference for earthquake models: A self-correcting model," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 337-347, July.
    • Handle: RePEc:eee:spapps:v:17:y:1984:i:2:p:337-347
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(84)90009-7
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harald Luschgy, 1993. "On a singularity occurring in a self-correcting point process model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 445-452, September.
    2. Frederic Schoenberg, 2002. "On Rescaled Poisson Processes and the Brownian Bridge," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 445-457, June.
    3. Takayuki Fujii & Yoichi Nishiyama, 2012. "Some problems in nonparametric inference for the stress release process related to the local time," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 991-1007, October.
    4. Nobuo Inagaki & Toshihabu Hayashi, 1990. "Parameter estimation for the simple self-correcting point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 89-98, March.
    5. F. Musmeci & D. Vere-Jones, 1992. "A space-time clustering model for historical earthquakes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 1-11, March.
    6. Vere-Jones, David, 1995. "Forecasting earthquakes and earthquake risk," International Journal of Forecasting, Elsevier, vol. 11(4), pages 503-538, December.

    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:spapps:v:17:y:1984:i:2:p:337-347. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/505572/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.