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Additional information for this article is available onlineincluding detailed proofs of the consistency results in lemmata 1,3, 4 and the weak convergence in the main result theorem 5. Furtherthe asymptotic validity of the bootstrap versions of the tests aresketched and it is demonstrated that an anlogous version ofStute’s (1997) test [see (1)] does not work in the context oftesting for monotonicity.

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