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

Emmanuelle Crétois

Applicationes Mathematicae (1995)

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

Abstract

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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).

How to cite

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Crétois, 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

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  1. [1] S. Abou-Jaoude, Convergence L 1 et L ∞ de certains estimateurs d’une densité de probabilité, thèse de doctorat d’état, Université Pierre et Marie Curie, 1979. 
  2. [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. [3] O. Kallenberg, Random Measures, 3rd ed., Akademie-Verlag, Berlin, and Academic Press, London. 
  4. [4] A. F. Karr, State estimation for Cox processes with unknown probability law, Stochastic Process. Appl. 20 (1985), 115-131. Zbl0578.60049
  5. [5] A. F. Karr, Point Processes and Their Statistical Inference, Marcel Dekker, New York, 1986. 

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