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On the power of nonparametric changepoint-tests. (English) Zbl 0804.62048
Summary: We consider a sequence $$X_{1n}, \dots, X_{mn}$$, $$n\in\mathbb{N}$$, of independent random elements. Suppose there exists a $$\theta\in [0,1)$$ such that $$X_{1n}, \dots, X_{[n\theta],n}$$ have the distribution $$\nu_ 1$$ and $$X_{[n\theta]+ 1,n}, \dots, X_{mn}$$ have the distribution $$\nu_ 2\neq \nu_ 1$$. We construct consistent level- $$\alpha$$ tests for $$H_ 0: \theta =0$$ versus $$H_ 1: \theta\in (0,1)$$, which are based on certain $$U$$-statistic type processes. A detailed investigation of the power function is also provided.

##### MSC:
 62G10 Nonparametric hypothesis testing 62M07 Non-Markovian processes: hypothesis testing 60F17 Functional limit theorems; invariance principles
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