Learning the regularity of multivariate functional data

2023/07/26 by Omar Kassi, Kassi, Omar, Nicolas Klutchnikoff +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #60G22 #62G07 #62M99 #62R10 #FOS: Computer and information sciences #FOS: Mathematics #Metabolomics and Mass Spectrometry Studies #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2307.14163

openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at possibly random discrete times. Non-asymptotic exponential bounds for the concentration of the regularity estimators are derived. An indicator for anisotropy is proposed and an exponential bound of its risk is derived. Two applications are proposed. We first consider the class of multi-fractional, bi-dimensional, Brownian sheets with domain deformation, and study the nonparametric estimation of the deformation. As a second application, we build minimax optimal, bivariate kernel estimators for the reconstruction of the surfaces.

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