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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  1. Brown M., 10.1214/aoms/1177693429, Ann. Math. Statist. 42 (1971), 773–776 (1971) Zbl0235.60044MR0343360DOI10.1214/aoms/1177693429
  2. Csiszár I., Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität Markoffscher Ketten, Publ. Math. Inst. Hungar. Acad. Sci., Ser. A 8 (1963), 85–108 (1963) MR0164374
  3. Jacod J., Shiryaev A. N., Limit Theorems for Stochastic Processes, Springer–Verlag, Berlin 1987 Zbl1018.60002MR0959133
  4. Karr A. F., Point Processes and their Statistical Inference, Marcel Dekker, New York 1986 Zbl0733.62088MR0851982
  5. Kutoyants, Yu. A., Parameter Estimation for Stochastic Processes, Helderman, Berlin 1984 Zbl0542.62073MR0777685
  6. Kutoyants, Yu. A., Statistical inference for spatial Poisson processes, Lab. de Stat. et Proc. Univ. du Maine, Le Mans, manuscript of forthcoming monography (1996) (1996) MR1644620
  7. LeCam L., Locally asymptotically normal families of distributions, Univ. Calif. Publ. Statist. 3 (1960), 37–98 (1960) MR0126903
  8. Liese F., 10.1002/mana.19750700116, Math. Nachr. 70 (1975), 183–196 (1975) Zbl0339.60052MR0478321DOI10.1002/mana.19750700116
  9. Liese F., 10.1080/02331888608801912, Statistics 17 (1986), 63–78 (1986) Zbl0598.60042MR0827946DOI10.1080/02331888608801912
  10. Liese F., Vajda I., Convex Statistical Distances, Teubner, Leipzig 1987 Zbl0656.62004MR0926905
  11. Lorz U., Sekundärgröen Poissonscher Punktprozesse – Grenzwertsätze und Abschätzungen der Konvergenzgeschwindigkeit, Rostock. Math. Kolloq. 29 (1986), 99–111 (1986) MR0863258
  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
  14. Mecke J., 10.1007/BF00535466, Z. Wahrsch. verw. Geb. 9 (1967), 36–58 (1967) MR0228027DOI10.1007/BF00535466
  15. Petrov V. V., Sums of Independent Random Variables, Akademie–Verlag, Berlin 1975 Zbl1125.60024MR0388499
  16. Strasser H., Mathematical Theory of Statistics, de Gruyter, Berlin 1985 Zbl0594.62017MR0812467
  17. Vajda I., Theory of Statistical Inference and Information, Kluwer, Dordrecht 1989 Zbl0711.62002

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