Elements of Statistics for Inference in Hilbert Spaces

Abstract

In this Master Project, two tests statistics for functional data are presented. A review of Hilbert space theory is given and fundamentals of probability in abstract spaces are presented. Then basic aspects of Functional Data Analysis are exposed, followed by some notions from inverse problems. Eventually a test for the mean of random curves, and for the Functional Linear Model with scalar responses are presented, with an application to DNA shape analysis.