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An application of $$U$$-statistics to change-point analysis. (English) Zbl 0832.62039
Summary: We obtain the necessary and sufficient condition for the weak convergence of $$U$$-statistic type processes in weighted metrics. The results are applied to the detection of changes in two data sets.

##### MSC:
 62G10 Nonparametric hypothesis testing 60F17 Functional limit theorems; invariance principles 60F05 Central limit and other weak theorems 62G20 Asymptotic properties of nonparametric inference