, Volume 14, Issue 1, pp 199–213 | Cite as

Estimation of the variance for a controlled branching process

  • Miguel González
  • Rodrigo Martínez
  • Iné del Puerto


In this paper we obtain estimators for the variance of the offspring distribution of a controlled branching process and we derive, for these estimators, some moments and asymptotic properties as consistency and limiting distribution.

Key Words

Branching processes method of moment estimators maximum likelihood estimators asymptotic behaviour 

AMS subject classification

60J80 62M05 


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  1. Bagley, J. H. (1986). On the almost sure convergence of controlled branching processes.Journal of Applied Probability, 23:827–831.MATHCrossRefMathSciNetGoogle Scholar
  2. Chow, Y. S. andTeicher, H. (1997).Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York, 3rd ed.MATHGoogle Scholar
  3. Dion, J. P. andEssebbar, B. (1995). On the statistics of controlled branching processes.Lecture Notes in Statistics, 99:14–21.MathSciNetGoogle Scholar
  4. González, M., Martínez, R., anddel Puerto, I. (2004). Nonparametric estimation of the offspring distribution and the mean for a controlled branching process.Test., 13(2):465–479.MATHCrossRefMathSciNetGoogle Scholar
  5. González, M., Molina, M., anddel Puerto, I. (2002). On the class of controlled branching processes with random control functions.Journal of Applied Probability, 39:804–815.MATHCrossRefMathSciNetGoogle Scholar
  6. González, M., Molina, M., anddel Puerto, I. (2003). On the geometric growth in controlled branching processes with random control function.Journal of Applied Probability, 40:995–1006.MATHCrossRefMathSciNetGoogle Scholar
  7. Guttorp, P. (1991)Statistical Inference for Branching Processes. John Wiley and Sons, Inc., New York.MATHGoogle Scholar
  8. Hall, P. andHeyde, C. C. (1980).Martingale Limit Theory and its Applications. Academic Press Inc., New York.Google Scholar
  9. Molina, M., González, M., andMota, M. (1998). Some theoretical results about superadditive controlled Galton-Watson branching processes. In M. Huskova, P. Lachout, and J. A. Visek, eds.,Proceedings of Prague Stochastic'98, vol. 1, pp. 413–418. Union of Czech Mathematicians and Physicist.Google Scholar
  10. Sevast'yanov, B. A. andZubkov, A. M. (1974). Controlled branching processes.Theory of Probability and its Applications, 19:14–24.CrossRefGoogle Scholar
  11. Yanev, N. M. (1975). Conditions for degeneracy of ϕ-branching processes with random ϕ.Theory of Probability and its Applications, 20:421–428.CrossRefGoogle Scholar
  12. Zubkov, A. M. (1974). Analogies between Galton-Watson processes and ϕ-branching processes.Theory of Probability and its Applications, 19:309–331.MATHCrossRefGoogle Scholar

Copyright information

© Sociedad Española de Estadistica e Investigacion Operativa 2005

Authors and Affiliations

  • Miguel González
    • 1
  • Rodrigo Martínez
    • 1
  • Iné del Puerto
    • 1
  1. 1.Departamento de MatemáticasUniversidad de ExtremaduraBadajozSpain

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