A0222
Title: Tests and confidence regions for incompletely observed functional data
Authors: David Kraus - Masaryk University (Czech Republic) [presenting]
Abstract: Methods are studied for the analysis of functional data under partial observation, by which we mean situations, where each functional variable may be observed only on a subset of the domain while no information about the function is available on the complement. Interestingly, some essential methods, such as K-sample tests of equal means or covariances and confidence intervals for eigenvalues and eigenfunctions, that are well established for completely observed curves, are lacking under the incomplete observation regime. The only currently available approach, in which incomplete curves are omitted, is clearly suboptimal and even infeasible, if there are no complete curves. We study methods that use all curve fragments and do not even require any complete curves. The principal difficulty in the practical implementation is the impossibility to perform dimension reduction, resulting in large objects that are often impossible to store in computer memory and perform computation with. The bootstrap turns out to be a way to address this problem. Theory, simulations and a data example will be presented.
