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Joint Estimation of Offspring Mean and Offspring Variance of Controlled Branching Process

Author

Listed:
  • Arpita Inamdar

    (Savitribai Phule Pune University (Formerly University of Pune))

  • Mohan Kale

    (Savitribai Phule Pune University (Formerly University of Pune))

Abstract

The paper discusses the joint estimation of two important parameters of the offspring distribution namely mean and variance of a controlled branching process or ϕ branching process. The estimation of these parameters was separately carried out by Gonzalez et al. (Test, 13(2), 465–479, (2004), Test, 14(1), 199–213, (2005)). The present article is an attempt to show that, the estimators proposed by these authors are also optimal in the sense of estimating functions (O F optimality). The joint O A optimality, that is; joint asymptotic properties of these estimators are also established using martingale limit theory. The joint O A optimality in special case, a model proposed by Dion and Essebbar (1995) for controlled branching process is also discussed.

Suggested Citation

  • Arpita Inamdar & Mohan Kale, 2016. "Joint Estimation of Offspring Mean and Offspring Variance of Controlled Branching Process," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 248-268, August.
    • Handle: RePEc:spr:sankha:v:78:y:2016:i:2:d:10.1007_s13171-016-0082-2
    DOI: 10.1007/s13171-016-0082-2
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    References listed on IDEAS

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    1. Miguel González & Rodrigo Martínez & Inés Puerto, 2004. "Nonparametric estimation of the offspring distribution and the mean for a controlled branching process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 465-479, December.
    2. Scott, D. J., 1978. "A central limit theorem for martingales and an application to branching processes," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 241-252, February.
    3. Miguel González & Rodrigo Martínez & Iné Puerto, 2005. "Estimation of the variance for a controlled branching process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 199-213, June.
    Full references (including those not matched with items on IDEAS)

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