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

Boumezoued, Alexandre; Hoffmann, Marc; Jeunesse, Paulien (2021), Nonparametric adaptive inference of birth and death models in a large population limit, Mathematical Statistics and Learning, 3, 1, p. 1-69. 10.4171/MSL/18

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1903.00673.pdf (812.3Kb)
Type
Article accepté pour publication ou publié
Date
2021
Journal name
Mathematical Statistics and Learning
Volume
3
Number
1
Publisher
European mathematical society
Pages
1-69
Publication identifier
10.4171/MSL/18
Metadata
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Author(s)
Boumezoued, Alexandre
R&D Milliman
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Jeunesse, Paulien
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Age-structured models; large population limit; concentration inequalities; nonparametric adaptive estimation; anisotropic estimation; Goldenshluger–Lepski method

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