COMPSTAT 2016: Start Registration
View Submission - CRoNoS FDA 2016
A0178
Title: Nonparametric registration to low-dimensional function spaces Authors:  Heiko Wagner - University of Bonn (Germany)
Alois Kneip - University of Bonn (Germany) [presenting]
Abstract: Registration aims to decompose amplitude and phase variation of samples of curves. Phase variation is captured by warping functions which monotonically transform the domains. Resulting registered curves should then only exhibit amplitude variation. Most existing registration method rely on aligning typical shape features like peaks or valleys to be found in each sample function. It is shown that this is not necessarily an optimal strategy for subsequent statistical data exploration and inference. In this context a major goal is to identify low dimensional linear subspaces of functions that areable to provide accurate approximations of the observed functional data. We present a registration method where warping functions are defined in such a way that the resulting registered curves span a low dimensional linear function space. Problems of identifiability are discussed in detail, and connections to established registration procedures are analyzed. Together with a suitable analysis of warping functions, the method allows to decompose functional data in a way that might be more informative than standard functional principal component analysis. We derive inference results for situations, where the true functions have to be reconstructed from discrete, noisy observations. The method is applied to real and simulated data.