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Register a new userNonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation
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Added by
Van Ha Hoang
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
Authors
Van Ha Hoang
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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.
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