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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Published electronically: June 10, 2004
MathSciNet review: 2000396
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Abstract | References | Similar Articles | 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.


References [Enhancements On Off] (What's this?)

  • 1. Marjorie Thomas, A generalization of Poisson’s binomial limit for use in ecology, Biometrika 36 (1949), 18–25. MR 0033999 (11,528d)
  • 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, Sluchainye protsessy s nezavisimymi prirashcheniyami, 2nd ed., \cyr Teoriya Veroyatnosteĭ\ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], “Nauka”, Moscow, 1986 (Russian). MR 860563 (88b:60171)
  • 4. Ju. M. Kabanov, R. Š. Lipcer, and A. N. Širjaev, Martingale methods in the theory of point processes, Proceedings of the School and Seminar on the Theory of Random Processes (Druskininkai, 1974) Inst. Fiz. i Mat. Akad. Nauk Litovsk. SSR, Vilnius, 1975, pp. 269–354 (Russian). MR 0431371 (55 #4371)
  • 5. I. A. Ibragimov and R. Z. Has′minskiĭ, Asimptoticheskaya teoriya otsenivaniya, “Nauka”, Moscow, 1979 (Russian). MR 545339 (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: http://dx.doi.org/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): 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