Issue |
ESAIM: PS
Volume 21, 2017
|
|
---|---|---|
Page(s) | 275 - 302 | |
DOI | https://doi.org/10.1051/ps/2017011 | |
Published online | 12 December 2017 |
Estimating the division kernel of a size-structured population
Laboratoire Paul Painlevé UMR CNRS 8524, Université de Lille 1, France.
van-ha.hoang@math.univ-lille1.fr
Received: 3 April 2017
Revised: 14 June 2017
Accepted: 14 June 2017
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.
Mathematics Subject Classification: 60J80 / 60J85 / 62G05 / 62G07 / 92D25
Key words: Random size-structured population / division kernel / nonparametric estimation / Goldenshluger-Lepski’s method / adaptive estimator / penalization
© EDP Sciences, SMAI, 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.