## Article

#### Title: Joint Estimation of Offspring Mean and Offspring Variance of Controlled Branching Process

##### Issue: Volume 78 Series A Part 2 Year 2016
###### 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 $\phi$ branching process. The estimation of these parameters was separately carried out by Gonzalez et al. (${\it Test}$, ${\bf 13}$(2), 465-479, (2004), ${\it Test}$, ${\bf 14}$(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.