On the power of nonparametric changepoint-tests

We consider a sequenceX1n,..., Xnn, n ∈ N, of independent random elements. Suppose there exists a θ∈[0, 1) such thatX1n,...,X(nθ),n have the distribution v1 andX[nθ]+1.n,...,Xnn have the distribution v2≠v1. We construct consistent level-α tests forH0:θ=0 versusH1:θ∈(0, 1), which are based on certainU-statistic type processes. A detailed investigation of the power function is also provided.

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