Dehling, HeroldSharipov, Olimjon Sh.Wendler, Martin2014-03-252014-03-252014-03-25http://hdl.handle.net/2003/3300010.17877/DE290R-13431Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an finite dimensional space is difficult, we show that the nonoverlapping block bootstrap is consistent. Furthermore, we show how these results can be used for degenerate von Mises-statistics.enDiscussion Paper / SFB 823;09/2014absolute regularityfunctional time seriesblock bootstrapHilbert spacenear epoch dependence310330620working paper