Valentin Patilea
CREST Ensai, Rennes, France

Combining information both within and between sample paths, we propose simple, nonparametric estimators for the local regularity of surfaces in 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. A diagnosis tool for checking anisotropy is proposed. A a first application, we consider the estimation of the parameters of a process from the class of multi-fractional Brownian sheets with time deformation. A second application is the adaptive, minimax optimal smoothing of surfaces.