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Article Dans Une Revue Mathematical Statistics and Learning Année : 2021

Nonparametric adaptive inference of birth and death models in a large population limit

Résumé

Motivated by improving mortality tables from human demography databases, we investigate statistical inference of a stochastic age-evolving density of a population alimented by time inhomogeneous mortality and fertility. Asymptotics are taken as the size of the population grows within a limited time horizon: the observation gets closer to the solution of the Von Foerster Mc Kendrick equation, and the difficulty lies in controlling simultaneously the stochastic approximation to the limiting PDE in a suitable sense together with an appropriate parametrisation of the anisotropic solution. In this setting, we prove new concentration inequalities that enable us to implement the Goldenshluger-Lepski algorithm and derive oracle inequalities. We obtain minimax optimality and adaptation over a wide range of anisotropic H\"older smoothness classes.

Dates et versions

hal-03064772 , version 1 (14-12-2020)

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Alexandre Boumezoued, Marc Hoffmann, Paulien Jeunesse. Nonparametric adaptive inference of birth and death models in a large population limit. Mathematical Statistics and Learning, 2021. ⟨hal-03064772⟩
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