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

Hoang, Van Ha; Pham Ngoc, Thanh Mai; Rivoirard, Vincent; Tran, Viet Chi (2022), Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation, Scandinavian Journal of Statistics, 49, 1, p. 4-43. 10.1111/sjos.12504

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Scandinavian Journal of Statistics
Volume
49
Number
1
Publisher
Wiley
Pages
4-43
Publication identifier
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Author(s)
Hoang, Van Ha
Laboratoire Paul Painlevé [LPP]
Pham Ngoc, Thanh Mai
Laboratoire de Mathématiques d'Orsay [LMO]
Rivoirard, Vincent
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tran, Viet Chi
Laboratoire Paul Painlevé [LPP]
Abstract (EN)
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.
Subjects / Keywords
Kernel rule; nonparametric estimation; cell division; deconvolution; Growth-fragmentation