2015/11/14 by Madison Giacofc, Sophie Lambert-Lacroix, Sophie Lambert‐Lacroix +4
Computer Science · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Methodology (stat.ME) #Statistical Methods and Inference #Statistical and numerical algorithms #stat.ME
paper · pdf · doi:10.48550/arxiv.1511.04556
arxiv created 2015/11/14 · openalex publication_date 2015/11/14 · arxiv updated 2015/11/17 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
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 L2 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 non parametric regression. Our approach is illustrated on realistic simulated datasets as well as on experimental data.