Advertisement

The asymptotic behaviour of maximum likelihood estimators for stationary point processes

  • Yoshiko Ogata
Article

Keywords

Point Process Maximum Likelihood Estimator Renewal Process Predictable Process Complete Intensity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Billingsley, P. (1961).Statistical Inference for Markov Process, The University of Chicago Press, ChicagoGoogle Scholar
  2. [2]
    Billingsley, P. (1961). The Lindeberg-Lévy Theorem for martingales,Proc. Amer. Math. Soc.,12, 788–792.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Dellacherie, C. (1972).Capacities et Processus Stochastiques, Springer-Verlag, Heidelberg.Google Scholar
  4. [4]
    Feller, W. (1966).An Introduction to Probability Theory and its Applications, Vol. 2. John Wiley & Sons, New York.Google Scholar
  5. [5]
    Hawkes, A. G. and Oakes, D. (1974). A cluster process representation of a self-exiting point process,J. Appl. Prob.,11, 493–503.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Kavanov, Yu. M., Lipster, R. Sh. and Shiryaev, A. N. (1975). Martingale method in the theory of point processes (in Russian),Proceeding of Vilnius Symposium U.S.S.R. Google Scholar
  7. [7]
    Meyer, P. A. (1972).Martingales and Stochastic Integrals I, Lecture Notes in Mathematics, 284, Springer, Berlin.Google Scholar
  8. [8]
    Ozaki, T. (1977). Maximum likelihood estimation of Hawkes' self-exciting point process,Research Memorandom, No. 115, The Institute of Statistical Mathematics, Tokyo.Google Scholar
  9. [9]
    Vere-Jones, D. (1973).Lectures on Point Processes, Department of Statistics, University of California, Berkeley.Google Scholar
  10. [10]
    Vere-Jones, D. (1975). On updating algorithms and inference for stochastic point processes,Perspectives in probability and statistics, Gani, J. ed., Applied Probability Trust.Google Scholar
  11. [11]
    Aczel, J. (1966).Lectures on Functional Equations and their Applications, Academic Press, New York.MATHGoogle Scholar
  12. [12]
    Daley, D. J. and Vere-Jones, D. (1972). A summary of the theory of point processes,Stochastic point processes: statistical analysis, theory and applications, Lewis, A. W. ed., Wiley, New York.Google Scholar
  13. [13]
    Huber, P. J. (1967). The behaviour of maximum likelihood estimates under nonstandard conditions,Proc. 5th Berkeley Symp. Math. Statist. Prob.,1, 221–233.MATHMathSciNetGoogle Scholar
  14. [14]
    Meyer, P. A. (1966).Probability and Potentials, Blaisdell Publishing Co., Waltham.MATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1978

Authors and Affiliations

  • Yoshiko Ogata
    • 1
  1. 1.Victoria University of WellingtonWellingtonAustralia

Personalised recommendations