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

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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.

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Authors and Affiliations

  1. Department of Statistics and Centre for Advanced Studies, Savitribai Phule Pune University (Formerly University of Pune), Ganeshkhind road, Pune, Maharashtra, 411007, India

    Arpita Inamdar & Mohan Kale

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  1. Arpita Inamdar
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  2. Mohan Kale
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Correspondence to Arpita Inamdar.

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Inamdar, A., Kale, M. Joint Estimation of Offspring Mean and Offspring Variance of Controlled Branching Process. Sankhya A 78, 248–268 (2016). https://doi.org/10.1007/s13171-016-0082-2

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