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Decemmber 2011 Asymptotic inference for partially observed branching processes
Andrea Kvitkovičová, Victor M. Panaretos
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Adv. in Appl. Probab. 43(4): 1166-1190 (Decemmber 2011). DOI: 10.1239/aap/1324045703


We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stochastic epidemic, allowing for the facts that only a part of the cases is detected, and that the detection mechanism may affect the evolution of the epidemic. In this setting, the offspring mean is closely related to the spreading potential of the disease, while the second moment is connected to the variability of the mean estimators. Inference for branching processes is known for its nonstandard characteristics, as compared with classical inference. When, in addition, the true process cannot be directly observed, the problem of inference suffers significant further perturbations. We propose nonparametric estimators related to those used when the underlying process is fully observed, but suitably modified to take into account the intricate dependence structure induced by the partial observation and the interaction scheme. We show consistency, derive the limiting laws of the estimators, and construct asymptotic confidence intervals, all valid conditionally on the explosion set.


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Andrea Kvitkovičová. Victor M. Panaretos. "Asymptotic inference for partially observed branching processes." Adv. in Appl. Probab. 43 (4) 1166 - 1190, Decemmber 2011.


Published: Decemmber 2011
First available in Project Euclid: 16 December 2011

zbMATH: 1230.62108
MathSciNet: MR2867950
Digital Object Identifier: 10.1239/aap/1324045703

Primary: 60J80, 62M05
Secondary: 60J85, 92D30

Rights: Copyright © 2011 Applied Probability Trust


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Vol.43 • No. 4 • Decemmber 2011
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