Branching processes random number of ancestors power series distribution paramertic estimation consistency asymptotic normality efficiency
Issue Date:
2005
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 17, No 1, (2005), 295p-312p
Abstract:
The paper deals with a parametric estimation in branching processes {Zt(n)} having random number of ancestors Z0(n) as both n and t tend to infinity (and thus Z0(n) in some sense). The offspring distribution is considered to belong to a discrete analogue of the exponential family - the class of the power series offspring distributions. Consistency and asymptotic normality of the estimators are obtained for all values of the offspring mean m, 0<m< , in the subcritical, critical and supercritical case.
