Metrika

, Volume 31, Issue 1, pp 349–360 | Cite as

Upper bound of the speed of convergence of moment density Estimators for stationary point processes

  • E. Jolivet
Publication

Summary

The speed of convergence of moment density estimators for stationary point processes is studied. Under relevant assumptions the order of magnitude for its upper bound is the same as in the i.i.d. case, when the process is Brillinger-mixing. The case of convariance density estimators is also considered.

Keywords

Point Process Density Estimator Covariance Measure Dirac Measure Global Risk 

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References

  1. Bretagnolle, J., andC. Huber: Estimation de densité: resque minimax. Z. Wahrscheinlichkeitstheorie und verw. Gebiete47, 1979, 119–137MathSciNetCrossRefMATHGoogle Scholar
  2. Brillinger, D.R.: Statistical inference for stationary point processes. In: Stochastic Processes and Related Topics, Vol. 1 (Puri, ed.). New York 1975, 55–92.Google Scholar
  3. Doukhan, P., andM. Ghindes: Etude des processus Xn=f(Xn−1)+n. Thèse de 3ème cycle, Paris XI, 1980.Google Scholar
  4. Jolivet, E.:Central limit theorem and convergence of empirical processes for stationary point processes. In: Point processes and Queuing Problems. Ed. by P. Bartfai and J. Tomko. Amsterdam 1980, 117–161.Google Scholar
  5. Krickeberg, K.: Statistique des processus ponctuels. Ecole d'Eté de St. Flour. Berlin 1982.Google Scholar

Copyright information

© Physica-Verlag 1984

Authors and Affiliations

  • E. Jolivet
    • 1
  1. 1.Laboratoire de Biométrie du C.N.R.Z.Jouy en JosasFrance

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