A0157
Title: Optimal inference for the mean of random functions
Authors: Valentin Patilea - CREST-Ensai (France) [presenting]
Abstract: The problem of estimating the mean of random functions defined on a multi-dimensional domain using discretely sampled data arises naturally in many applications. The estimation and inference for the mean function are studied under random design. The number of design points on each curve is allowed to be as small as 1. New optimal rate estimators based on Fourier series are proposed, and non-asymptotic bounds are given for both the $L^2$ norm and the uniform norm. Inference is also constructed. An estimator of the regularity of the mean curve is presented, making this approach adaptive.
