# Statistical estimation in a randomly structured branching population

3 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
LAPM - Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble], Inria Grenoble - Rhône-Alpes, Institut Jean Roget
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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https://hal.archives-ouvertes.fr/hal-01662203
Contributor : Aline Marguet <>
Submitted on : Monday, February 25, 2019 - 9:54:20 PM
Last modification on : Wednesday, November 4, 2020 - 3:30:20 PM

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### Citation

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

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