Title: Robust change point tests using bounded transformations
Authors: Alexander Duerre - TU Dortmund (Germany) [presenting]
Roland Fried - TU Dortmund University (Germany)
Daniel Vogel - University of Aberdeen (United Kingdom)
Abstract: Classical moment based change point tests like the cusum test are very powerful under Gaussian time series with no more than one change point but behave poorly under heavy tailed distributions and corrupted data. A new class of robust change point tests based on cusum statistics of robustly transformed observations is proposed. This framework is very flexible, depending on the used transformation one can detect amongst others changes in the mean, scale or dependence of a possibly multivariate time series. The calculation of $p$-values can be simplified by using asymptotics which yields a computational complexity of $T\log(T)$ where $T$ is the number of observations. Symmetrization leads to change point tests based on U-Statistics, which are more powerful under Gaussianity but less robust and have a complexity of $T^2.$ The application of both approaches is illustrated on the basis of some examples which are evaluated using the statistical software R.