Nonparametric estimation of the fragmentation kernel based on a partial differential equation stationary distribution approximation

Hoang Van Ha, Thanh Mai Pham Ngoc, Vincent Rivoirard and Viet Chi Tran

Scandinavian Journal of Statistics, 2022, vol. 49, issue 1, 4-43

Abstract: We consider a stochastic individual‐based model in continuous time to describe a size‐structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We here address the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves a multiplicative deconvolution operator. Using Fourier techniques we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the nonstandard equations connecting the Fourier transforms of the kernel and the parameters of the model. A numerical study is carried out and we pay special attention to the derivation of bandwidths by using resampling.

Date: 2022
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