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

Arpita Inamdar () and Mohan Kale ()
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Arpita Inamdar: Savitribai Phule Pune University (Formerly University of Pune)
Mohan Kale: Savitribai Phule Pune University (Formerly University of Pune)

Sankhya A: The Indian Journal of Statistics, 2016, vol. 78, issue 2, No 6, 248-268

Abstract: 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.

Keywords: Estimating equations; Joint asymptotic normality; Martingale convergence theorem; Martingale central limit theorem; 60J80; 62M05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13171-016-0082-2

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