Geodesic
Estimating the division kernel of a size-structured population
Hoang, Van Ha1  
1 Laboratoire Paul Painlevé UMR CNRS 8524, Université de Lille 1, France.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 275-302

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We consider a size-structured model describing a population of cells proliferating by division. Each cell contain a quantity of toxicity which grows linearly according to a constant growth rate α. At division, the cells divide at a constant rate R and share their content between the two daughter cells into fractions Γ and 1-Γ where Γ has a symmetric density h on [0,1], since the daughter cells are exchangeable. We describe the cell population by a random measure and observe the cells on the time interval [0,T] with fixed T. We address here the problem of estimating the division kernel h (or fragmentation kernel) when the division tree is completely observed. An adaptive estimator of h is constructed based on a kernel function K with a fully data-driven bandwidth selection method. We obtain an oracle inequality and an exponential convergence rate, for which optimality is considered.

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Accepté le :
DOI : 10.1051/ps/2017011
Classification : 60J80, 60J85, 62G05, 62G07, 92D25
Keywords: Random size-structured population, division kernel, nonparametric estimation, Goldenshluger-Lepski’s method, adaptive estimator, penalization

Hoang, Van Ha 1

1 Laboratoire Paul Painlevé UMR CNRS 8524, Université de Lille 1, France. 
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     title = {Estimating the division kernel of a size-structured population},
     journal = {ESAIM: Probability and Statistics},
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     publisher = {EDP-Sciences},
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     zbl = {1393.60096},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2017011/}
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Hoang, Van Ha. Estimating the division kernel of a size-structured population. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 275-302. doi: 10.1051/ps/2017011

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