Asymptotic efficiency of statistical estimates in a compound Poisson model
Authors:
O. G. Kukush and Yu. S. Mishura
Translated by:
Yu. Mishura
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal:
Theor. Probability and Math. Statist. 68 (2004), 67-80
MSC (2000):
Primary 62F10, 62F12, 60G55
DOI:
https://doi.org/10.1090/S0094-9000-04-00607-6
Published electronically:
June 10, 2004
MathSciNet review:
2000396
Full-text PDF Free Access
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Additional Information
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.
1 M. Thomas, A generalization of Poisson’s binomial limit for use in ecology, Biometrica 36 (1949), 18–25.
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- A. V. Skorokhod, Sluchaĭ nye protsessy s nezavisimymi prirashcheniyami, 2nd ed., Teoriya Veroyatnosteĭ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], “Nauka”, Moscow, 1986 (Russian). MR 860563
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- I. A. Ibragimov and R. Z. Has′minskiĭ, Asimptoticheskaya teoriya otsenivaniya, “Nauka”, Moscow, 1979 (Russian). MR 545339
1 M. Thomas, A generalization of Poisson’s binomial limit for use in ecology, Biometrica 36 (1949), 18–25.
2 A. C. Gleeson and I. B. Douglas, Quadrat sampling and the estimation of Neyman type A and Thomas distributional parameters, Austral. J. Statist. 17 (1975), no. 2, 103–113.
3 A. V. Skorokhod, Stochastic Processes with independent Increments, “Nauka”, Moscow, 1986; English transl., Kluwer, Dordrecht, 1991.
4 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.
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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
Keywords:
Compound Poisson process,
statistical estimates,
asymptotic efficiency,
local asymptotic normality
Received by editor(s):
May 7, 2002
Published electronically:
June 10, 2004
Additional Notes:
The work is partially supported by INTAS grant No. 99-000-16.
Article copyright:
© Copyright 2004
American Mathematical Society
