Geodesic
Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors
Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 243-262.

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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.
Keywords: Branching Processes, Random Number of Ancestors, Power Series Distribution, Parametric Estimation, Robustness, D-Fullness 
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     author = {Stoimenova, Vessela},
     title = {Robust {Parametric} {Estimation} of {Branching} {Processes} with a {Random} {Number} of {Ancestors}},
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Stoimenova, Vessela. Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors. Serdica Mathematical Journal, Tome 31 (2005) no. 3, pp. 243-262. http://geodesic.mathdoc.fr/item/SMJ2_2005_31_3_a5/