Contiguity and LAN-property of sequences of Poisson processes

Friedrich Liese; Udo Lorz

Kybernetika (1999)

  • Volume: 35, Issue: 3, page [281]-308
  • ISSN: 0023-5954

Abstract

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Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.

How to cite

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Liese, Friedrich, and Lorz, Udo. "Contiguity and LAN-property of sequences of Poisson processes." Kybernetika 35.3 (1999): [281]-308. <http://eudml.org/doc/33429>.

@article{Liese1999,
abstract = {Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.},
author = {Liese, Friedrich, Lorz, Udo},
journal = {Kybernetika},
keywords = {Poisson point process; local asymptotic normality; Hellinger integral; likelihood ratio; Poisson point process; local asymptotic normality; Hellinger integral; likelihood ratio},
language = {eng},
number = {3},
pages = {[281]-308},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Contiguity and LAN-property of sequences of Poisson processes},
url = {http://eudml.org/doc/33429},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Liese, Friedrich
AU - Lorz, Udo
TI - Contiguity and LAN-property of sequences of Poisson processes
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 3
SP - [281]
EP - 308
AB - Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.
LA - eng
KW - Poisson point process; local asymptotic normality; Hellinger integral; likelihood ratio; Poisson point process; local asymptotic normality; Hellinger integral; likelihood ratio
UR - http://eudml.org/doc/33429
ER -

References

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  12. Lorz U., Beiträge zur Statistik unbegrenzt teilbarer Felder mit unabhängigen Zuwächsen, Dissertation, Univ. Rostock 1987 Zbl0682.62072
  13. Lorz U., Heinrich L., 10.1080/02331889108802342, Statistics 22 (1991), 627– 649 (1991) MR1128489DOI10.1080/02331889108802342
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