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Asymptotic efficiency of statistical estimates in a compound Poisson model

Author(s): O. G. Kukush; Yu. S. Mishura
Translated by: Yu. Mishura
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 68 (2003).
Journal: Theor. Probability and Math. Statist. No. 68 (2004), 67-80.
MSC (2000): Primary 62F10, 62F12, 60G55
Posted: June 10, 2004
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Abstract: We consider maximum likelihood statistical estimates for the number of individuals in a biological population modelled by a compound Poisson process. We prove the local asymptotic normality and asymptotic efficiency of the estimates.

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Yu. M. Kabanov, R. S. Liptzer, and A. N. Shiryaev, Martingale methods in the theory of point processes, Proceedings of the School-Seminar on the Theory of Random Processes, Part II, Vilnius, 1975, pp. 269-354. MR 55:4371

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I. A. Ibragimov and R. Z. Khas'minski{\u{\i}}\kern.15em, Statistical Estimation: Asymptotic Theory, ``Nauka", Moscow, 1979; English transl., Springer-Verlag, Berlin-Heidelberg-New York, 1981. MR 81h:62004

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Additional Information:

O. G. Kukush
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics and Mechanics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv--127 03127, Ukraine
Email: Alexander_Kukush@univ.kiev.ua

Yu. S. Mishura
Affiliation: Department of Mathematical Analysis, Faculty for Mathematics and Mechanics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv--127 03127, Ukraine
Email: myus@univ.kiev.ua

DOI: 10.1090/S0094-9000-04-00607-6
PII: S 0094-9000(04)00607-6
Keywords: Compound Poisson process, statistical estimates, asymptotic efficiency, local asymptotic normality
Received by editor(s): 7/MAY/2002
Posted: June 10, 2004
Additional Notes: The work is partially supported by INTAS grant No. 99-000-16.
Copyright of article: Copyright 2004, American Mathematical Society

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