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Inference for earthquake models: A self-correcting model

Author

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  • 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
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    Citations

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    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. 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.
    4. Vere-Jones, David, 1995. "Forecasting earthquakes and earthquake risk," International Journal of Forecasting, Elsevier, vol. 11(4), pages 503-538, December.
    5. 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.
    6. 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.

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