Branching Processes Random Number of Ancestors Power Series Distribution Parametric Estimation Robustness D-Fullness
Issue Date:
2005
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 31, No 3, (2005), 243p-262p
Abstract:
The paper deals with a robust parametric estimation in branching processes {Zt(n)} having a 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. Robust estimators, based on one and several sample paths, are proposed and studied for all values of the offspring mean m, 0 < m < ∞, in the subcritical, critical and supercritical case.
