Abstract
We investigate the large-sample behavior of change-point tests based on weighted two-sample U-statistics, in the case of short-range dependent data. Under some mild mixing conditions, we establish convergence of the test statistic to an extreme value distribution. A simulation study shows that the weighted tests are superior to the non-weighted versions when the change-point occurs near the boundary of the time interval, while they loose power in the center.
Highlights
We study nonparametric tests for change-points in time series that are based on weighted two-sample U -statistics
By the choice of the kernel function h, the weighted two-sample U-statistics lead to a flexible class of change-point tests
Considering data with heavier tails, such as t(5) or t(3) distributed observations, one can see that the CUSUM test statistics lose more power, especially the weighted CUSUM
Summary
We study nonparametric tests for change-points in time series that are based on weighted two-sample U -statistics. By a suitable choice of the weights, we obtain tests that are able to detect changes that occur very early or very late during the observation period. Our results cover both the CUSUM test and the Wilcoxon change-point test, as well as many other robust and nonrobust tests. Csorgoand Horvath [2] investigated U-statistics with general kernels, in the case of independent data They could show that the asymptotic distribution under the null hypothesis is the Kolmogorov-Smirnov distribution, which is the distribution of the supremum of a Brownian bridge. By the choice of the kernel function h, the weighted two-sample U-statistics lead to a flexible class of change-point tests. Full details of the proofs are presented in the final section
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