Skip to main content
Log in

Asymptotic parameter estimation for multivariate point processes

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. I. A. Ibragimov and R. Z. Hasminskii,Statistical Estimation: Asymptotic Theory, Springer-Verlag, Berlin-Heidelberg-New York (1981).

    Google Scholar 

  2. Yu. A. Kutoyants,Parameter Estimation of Random Processes. Asymptotic Theory, Doctor Thesis, Leningrad (1987).

  3. Yu. A. Kutoyants,Parameter Estimation of Random Processes [in Russian], Izd. AN Arm. SSR, Ervan (1980).

    Google Scholar 

  4. Yu. A. Kutoyants, Estimation of parameters of processes of Poisson type,Sov. J. Contemp. Math. Anal., Arm. Acad. Sci.,19(3), 47–55 (1984).

    MATH  MathSciNet  Google Scholar 

  5. Yu. N. Linkov,Asymptotic Methods of Statistics of Random Processes [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  6. Yu. N. Linkov, Estimates of parameters of counting processes,Probl. Inf. Transm.,18, 63–76 (1982).

    MATH  MathSciNet  Google Scholar 

  7. Yu. M. Kabanov, R. S. Liptser and A. N. ShiryaevCriteria of Absolute Continuity of Measures Corresponding to Multivariate Point Processes, Lecture Notes in Mathematics 550, Springer, Berlin, 232–252 (1976).

    Google Scholar 

  8. Yu. M. Kabanov, R. Sh. Liptser and A. N. Shiryaev, Absolute continuity and singularity of locally absolutely continuous distributions, I, II,Math. USSR, Sb.,35, 631–680;36 (1980), 31–58 (1979).

    Article  Google Scholar 

  9. R. Sh. Liptser and A. N. Shiryaev,Theory of Martingales [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  10. Yu. M. Kabanov, R. Sh. Liptser and A. N. Shiryaev, Martingale methods in the theory of point processes, II, in:Trudy Shkoly-Seminara po Teorii Sluchainykh Protsessov, Vilnius (1975), pp. 269–354.

  11. J. Jacod, Multivariate point processes: predictable projection, Radon-Nicodym derivatives, representation of martingales,Z. Wahr. verw. Geb.,34, 235–253 (1975).

    Article  Google Scholar 

  12. J. Jacod and A. N. Shiryaev,Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin-Heidelberg-New York (1987).

    Google Scholar 

  13. A. F. Karr,Point Processes and Their Statistical Inference, Marcel Dekker, New York (1986).

    Google Scholar 

  14. A. Sieders and K. Dzhaparidze, A large deviation result for parameter estimators and its application to nonlinear regression analysis.Ann. Statist.,15, 1031–1049 (1987).

    MATH  MathSciNet  Google Scholar 

  15. K. Dzhaparidze and E. Valkeila, On large deviation probabilities for the maximum likelihood estimators, in:Probab. Theory and Math. Statist., Vol. 1, B. Grigelioniset al. (Eds.), VSP/Mokslas (1990), pp. 285–292.

  16. E. Valkeila,A Note on Large Deviation Probabilities for the Maximum Likelihood Estimator in Filtered Experiments, Computing Centre, P.O. Box 26, FIN-00014, University of Helsinki (1995).

Download references

Authors

Additional information

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 37, No. 4, pp. 467–482, October–December, 1997.

Translated by V. Mackevičius

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kanišauskas, V. Asymptotic parameter estimation for multivariate point processes. Lith Math J 37, 352–363 (1997). https://doi.org/10.1007/BF02465576

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02465576

Keywords

Navigation