Statistical estimation in a randomly structured branching population

Marc Hoffmann and Aline Marguet

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 5236-5277

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.

Keywords: Branching processes; Bifurcating Markov chains; Statistical estimation; Geometric ergodicity; Scalar diffusions (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2019.02.015

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