A1345
Title: Fast rate estimation of integrals of multivariate random functions
Authors: Sunny Wang - ENSAI (France) [presenting]
Valentin Patilea - CREST-Ensai (France)
Abstract: The problem of estimating integrals of random functions defined on a compact interval or multidimensional rectangle arises naturally in functional data analysis. Such integrals are needed to make predictions using functional regression models, to compute the scores of a random function in a basis, to compute data depths, etc. Using a recent linear integration approach from the Monte Carlo literature, a new class of estimators is proposed in the case where the random functions are observed, possibly with measurement noise, on a discrete, random set of design points. In the absence of noise, the estimators converge faster than the empirical means. Narrow confidence intervals are proposed both with and without measurement noise.
