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Statistical estimation in a randomly structured branching population

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

Type
Article accepté pour publication ou publié
Date
2019
Journal name
Stochastic Processes and their Applications
Volume
129
Number
12
Publisher
Elsevier
Pages
5236-5277
Publication identifier
Metadata
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Author(s)
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Marguet, Aline
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Abstract (EN)
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.
Subjects / Keywords
statistical estimation; Branching processes; bifurcating Markov chains; geometric ergodicity; scalar diffusions