B0815
Title: Learning the regularity of multivariate functional data
Authors: Omar Kassi - (ENSAI) Ecole Nationale de la Statistique et de l'Analyse de l'Information (France) [presenting]
Abstract: Combining information within and between sample paths, a simple estimator is proposed for the local regularity of surfaces in a two-dimensional functional data framework. The independently generated surfaces are measured with error 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. The class of multi-fractional Brownian sheets with domain deformation are first considered, and nonparametric estimators are studied for the Hurst exponent function and the domain deformation. As a second application, minimax optimal kernel estimators are built for the reconstruction of the surfaces.
