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

Alexandre Boumezoued; Marc Hoffmann; Paulien Jeunesse

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arXiv · 1903.00673

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

Alexandre Boumezoued·Marc Hoffmann·Paulien Jeunesse

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Abstract

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.

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Alexandre Boumezoued, Marc Hoffmann, Paulien Jeunesse. 2019-03-02. Nonparametric adaptive inference of birth and death models in a large population limit. https://arxiv.org/abs/1903.00673

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