Estimating the Division Kernel of a Size-Structured Population

TL;DR

This paper develops an adaptive, data-driven method to estimate the division kernel in size-structured cell populations, providing theoretical guarantees and optimal convergence rates.

Contribution

It introduces a novel adaptive estimator for the division kernel with a fully data-driven bandwidth selection, along with theoretical performance guarantees.

Findings

Achieves an oracle inequality for the estimator.

Provides an exponential convergence rate.

Demonstrates optimality of the estimator.

Abstract

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.