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We consider a size-structured population describing the cell divisions. Thecell population is described by an empirical measure and we observe thedivisions in the continuous time interval [0, T ]. We address here the problemof estimating the division kernel h (or fragmentation kernel) in case ofcomplete data. An adaptive estimator of h is constructed based on a kernelfunction K with a fully data-driven bandwidth selection method. We obtain anoracle inequality and an exponential convergence rate, for which optimality isconsidered.

Estimating the Division Kernel of a Size-Structured Population