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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.

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