Estimating the Division Kernel of a Size-Structured Population

van Ha Hoang (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We consider a size-structured population describing the cell divisions. The cell population is described by an empirical measure and we observe the divisions in the continuous time interval [0, T ]. We address here the problem of estimating the division kernel h (or fragmentation kernel) in case of complete data. 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.

Mots clés: random size-structured population; nonparametric estimation; optimal rate; penalization; adaptive estimator; Goldenshluger-Lepski's method; division kernel

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

van Ha Hoang. Estimating the Division Kernel of a Size-Structured Population. 2015. ⟨hal-01196427v4⟩