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Journal Articles Stochastic Processes and their Applications Year : 2019

Statistical estimation in a randomly structured branching population

Abstract

We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the observation of the trait at birth of the first n generations of the process, we construct nonparametric estimator of the transition of the associated bifurcating chain and study the parametric estimation of the branching rate. In the limit $n → ∞$, we obtain asymptotic efficiency in the parametric case and minimax optimality in the nonparametric case.
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Dates and versions

hal-01662203 , version 1 (12-12-2017)
hal-01662203 , version 2 (19-11-2018)
hal-01662203 , version 3 (25-02-2019)

Identifiers

Cite

Marc Hoffmann, Aline Marguet. Statistical estimation in a randomly structured branching population. Stochastic Processes and their Applications, 2019, 129 (12), pp.5236-5277. ⟨10.1016/j.spa.2019.02.015⟩. ⟨hal-01662203v3⟩
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