Nonparametric adaptive inference of birth and death models in a large population limit
| Autor: | Paulien Jeunesse, Alexandre Boumezoued, Marc Hoffmann |
|---|---|
| Přispěvatelé: | R&D Milliman, Milliman, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
education.field_of_study
Smoothness (probability theory) Population Inference Mathematics - Statistics Theory Statistics Theory (math.ST) Minimax Stochastic approximation Birth–death process [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] FOS: Mathematics Statistical inference Applied mathematics Quantitative Biology::Populations and Evolution Limit (mathematics) education Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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