Title: Robust detection for change-points in functional time series based on spatial signs and bootstrap
Authors: Lea Wegner - Otto-von-Guericke University Magdeburg (Germany) [presenting]
Martin Wendler - Otto-von-Guericke University Magdeburg (Germany)
Abstract: One main strategy in changepoint detection for time series is to project the data on a finite-dimensional space with techniques such as functional principal components. In contrast, there are recent proposals to base the statistical tests on the full functional information, typically modeled as Hilbert-space-valued time series. Up to now, test statistics for changepoint detection in functional time series are based on sample means and outliers can influence the test result. Generalizing the Wilcoxon statistic, we have constructed a new functional version of a two-sample U-statistic with a bounded antisymmetric kernel. We will present limit theorems for U-statistics with values in Hilbert spaces and deduce the asymptotic distribution of our changepoint statistic. Because of the boundedness of the kernel, the statistic is indeed robust against outliers. Since this class of test statistics does not rely on dimension reduction, the limit distribution provides an infinite-dimensional covariance operator as a parameter, which is difficult to estimate. Because of this, we propose a new variant of the dependent wild bootstrap adapted to U-statistics in Hilbert spaces.