B0892
Title: First versus full or first versus last: U-statistic change-point tests under fixed and local alternatives
Authors: Daniel Vogel - MEDICE Arzneimittel Pütter (Germany) [presenting]
Herold Dehling - Ruhr-University Bochum (Germany)
Martin Wendler - Otto-von-Guericke University Magdeburg (Germany)
Abstract: The use of U-statistics in the change-point context has received considerable attention in the literature. Two approaches for constructing CUSUM-type change-point tests are compared, which are called the first-vs-full and first-vs-last approaches. Both have been pursued by different authors. The question naturally arises if the two tests substantially differ and, if so, which of them is better in which data situation. In large samples, both tests are similar: they are asymptotically equivalent under the null hypothesis and under sequences of local alternatives. In small samples, there may be quite noticeable differences, which is in line with different asymptotic behavior under fixed alternatives. A simple criterion is derived for deciding which test is more powerful. Several examples are examined in detail. Particularly, when testing for changes in scale by Gini's mean difference, it is shown that the first-vs-full approach has a higher power if and only if the scale changes from a small to a larger value, regardless of the population distribution or the location of the change. All asymptotic derivations are under weak dependence. The results are illustrated by numerical simulations and data examples.
