Minimax wavelet estimation for multisample heteroscedastic non-parametric regression [article]

Madison Giacofc and Sophie Lambert-Lacroix and Franck Picard
2015 arXiv   pre-print
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 L_2 minimax risk is provided, as well as the upper bound of the minimax rate, that is derived by constructing a wavelet estimator for the
more » ... ctional fixed effect. Our work constitutes the first theoretical functional results in multisample non parametric regression. Our approach is illustrated on realistic simulated datasets as well as on experimental data.
arXiv:1511.04556v1 fatcat:2mfmi4gpt5bwfhdilhecgij5ce