Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation

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 address here 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 technics we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the non-standard 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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01623403
Contributeur : Van Ha Hoang <>
Soumis le : mercredi 25 octobre 2017 - 11:42:06
Dernière modification le : lundi 30 avril 2018 - 14:52:03
Document(s) archivé(s) le : vendredi 26 janvier 2018 - 13:30:32

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  • HAL Id : hal-01623403, version 1
  • ARXIV : 1710.09172

Citation

Van Ha Hoang, Thanh Mai Pham Ngoc, Vincent Rivoirard, Viet Chi Tran. Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation. 2017. 〈hal-01623403〉

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