Minimax wavelet estimation for multisample heteroscedastic nonparametric regression

Madison Giacofci (1, 2) , Sophie Lambert-Lacroix (3) , Franck Picard (4)

1 LJK - Laboratoire Jean Kuntzmann
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 TIMC-IMAG-BCM - Biologie Computationnelle et Mathématique
4 LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558

The problem of estimating the baseline signal from multisample noisy curves is investigated. We consider the functional mixed-effects model, and we suppose that the functional fixed effect belongs to the Besov class. This framework allows us to model curves that can exhibit strong irregularities, such as peaks or jumps for instance. The lower bound for the minimax risk is provided, as well as the upper bound of the minimax rate, that is derived by constructing a wavelet estimator for the functional fixed effect. Our work constitutes the first theoretical functional results in multisample nonparametric regression. Our approach is illustrated on realistic simulated datasets as well as on experimental data.

Keywords: Functional mixed-effects models; minimax risk; Besov class; wavelet estimator

Domains: Life Sciences [q-bio]

Madison Giacofci, Sophie Lambert-Lacroix, Franck Picard. Minimax wavelet estimation for multisample heteroscedastic nonparametric regression. Journal of Nonparametric Statistics, 2018, 30 (1), pp.238-261. ⟨10.1080/10485252.2017.1406091⟩. ⟨hal-02270811⟩