Robust and nonparametric detection of shifts using two-sample U-statistics and U-quantiles

Roland Fried (TU Dortmund)
Wednesday, January 13, 2016 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Tests for detecting level shifts in near epoch dependent time series are studied. The popular CUSUM test is not robust to outliers and can be improved in case of non-normal data, particularly for heavy-tails. The CUSUM test can be modified using the Hodges-Lehmann 2-sample estimator, which is the median of all pairwise differences between the samples. It is highly robust and has a high efficiency under normality. Like for a related test based on the 2-sample Wilcoxon statistic, the asymptotics of the Hodges-Lehmann change-point test can be established under general conditions without any moment assumptions. Both tests offer similar power against shifts in the center of the data, but the test based on the Hodges-Lehmann estimator performs superior if a shift occurs far from the center. As a further variant of change-point tests, we study MOSUM-type tests which restrict attention to data in two subsequent moving time windows. This may overcome possible masking eects due to several shifts into different directions.
Co-authors: Herold Dehling (Ruhruniversität Bochum) , Martin Wendler (Universität Greifswald)