Title: Functional data analysis for continuous functions
Authors: Holger Dette - Ruhr-Universitaet Bochum (Germany) [presenting]
Abstract: The aim is to develop data analysis methodology for functional time series in the space of all continuous functions. Our methodology is motivated by the fact that objects with rather different shapes may still have a small $L_2$-distance and are therefore identified as similar when using an $L_2$-metric. However, in applications it is often desirable to use metrics reflecting the visualization of the curves in the statistical analysis. The methodological contributions are focused on developing two-sample and change-point tests as well as confidence bands, as these procedures appear to be conducive to the proposed setting. Particular interest is put on relevant differences; that is, on not trying to test for exact equality, but rather for pre-specified deviations under the null hypothesis. The procedures are justified through large-sample theory. To ensure practicability, non-standard bootstrap procedures are developed and investigated addressing particular features that arise in the problem of testing relevant hypotheses. The finite sample properties are explored through a simulation study.