Orateur
Description
We introduce a new notion of regularity, called directional regularity, which is rele- vant for a wide range of applications involving multivariate functional data. We show that for anisotropic functional data, faster rates of convergence can be obtained by adapting to its directional regularity through a change of basis. An algorithm is constructed for the estimation and identification of the directional regularity for a large class of stochastic processes, made possible due to the unique replication nature of functional data. Accompanying non-asymptotic theoretical guarantees are provided. A novel simulation algorithm, which is of independent interest, is designed to evaluate the numerical accuracy of our directional regularity algorithm. Simulation results demon- strate the good finite sample properties of our estimator, which is freely available in the R package direg.
