Statistical estimation in a randomly structured branching population

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Hoffmann, Marc¹  Marguet, Aline² 

[1] Univ Paris Dauphine PSL, CEREMADE, F-75016 Paris, France

[2] Univ Grenoble Alpes, INRIA, F-38000 Grenoble, France

关键词: Branching processes;    Bifurcating Markov chains;    Statistical estimation;    Geometric ergodicity;    Scalar diffusions;   

DOI  :  10.1016/j.spa.2019.02.015

来源: Elsevier

【 摘 要 】

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 -> infinity, we obtain asymptotic efficiency in the parametric case and minimax optimality in the nonparametric case. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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