The purpose of the paper is to investigate weak asymptotic behaviour of rank statistics proposed for detection of gradual changes, linear trends in particular. The considered statistics can be used for various test procedures. The fundaments of the proofs are formed by results of Hušková [4] and Jarušková [5].
Approximations to the critical values for tests for multiple changes in location models are obtained through permutation tests principle. Theoretical results say that the approximations based on the limit distribution and the permutation distribution of the test statistics behave in the same way in the limit. However, the results of simulation study show that the permutation tests behave considerably better than the corresponding tests based on the asymptotic critical value.
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