# Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law

Applicationes Mathematicae (1995)

- Volume: 23, Issue: 3, page 247-259
- ISSN: 1233-7234

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topCrétois, Emmanuelle. "Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law." Applicationes Mathematicae 23.3 (1995): 247-259. <http://eudml.org/doc/219129>.

@article{Crétois1995,

abstract = {Let $N_i$, i ≥ 1, be i.i.d. observable Cox processes on [a,b] directed by random measures Mi. Assume that the probability law of the Mi is completely unknown. Random techniques are developed (we use data from the processes $N_1$,..., $N_n$ to construct a partition of [a,b] whose extremities are random) to estimate L(μ,g) = E(exp(-(N(g) - μ(g))) | N - μ ≥ 0).},

author = {Crétois, Emmanuelle},

journal = {Applicationes Mathematicae},

keywords = {random partition; Cox processes; reduced Palm processes; random measures},

language = {eng},

number = {3},

pages = {247-259},

title = {Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law},

url = {http://eudml.org/doc/219129},

volume = {23},

year = {1995},

}

TY - JOUR

AU - Crétois, Emmanuelle

TI - Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law

JO - Applicationes Mathematicae

PY - 1995

VL - 23

IS - 3

SP - 247

EP - 259

AB - Let $N_i$, i ≥ 1, be i.i.d. observable Cox processes on [a,b] directed by random measures Mi. Assume that the probability law of the Mi is completely unknown. Random techniques are developed (we use data from the processes $N_1$,..., $N_n$ to construct a partition of [a,b] whose extremities are random) to estimate L(μ,g) = E(exp(-(N(g) - μ(g))) | N - μ ≥ 0).

LA - eng

KW - random partition; Cox processes; reduced Palm processes; random measures

UR - http://eudml.org/doc/219129

ER -

## References

top- [1] S. Abou-Jaoude, Convergence ${L}_{1}$ et ${L}_{\infty}$ de certains estimateurs d’une densité de probabilité, thèse de doctorat d’état, Université Pierre et Marie Curie, 1979.
- [2] E. Crétois, Estimation de la densité moyenne d'un processus ponctuel de Poisson par des méthodes aléatoires, Congrès des XXIVèmes Journées de Statistique de Bruxelles, Mai 1992.
- [3] O. Kallenberg, Random Measures, 3rd ed., Akademie-Verlag, Berlin, and Academic Press, London.
- [4] A. F. Karr, State estimation for Cox processes with unknown probability law, Stochastic Process. Appl. 20 (1985), 115-131. Zbl0578.60049
- [5] A. F. Karr, Point Processes and Their Statistical Inference, Marcel Dekker, New York, 1986.

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