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Keywords:
gradual type of change; location model; rank statistics; weighted suprema; limit theorems
gradual type of change; location model; rank statistics; weighted suprema; limit theorems
Summary:
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].
References:
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[2] Einmahl U.: A useful estimate in the multidimensional invariance principle. Probab. Theory Related Fields (1987), 76 81-101. MR 0899446 | Zbl 0608.60029
[3] Hájek J., Šidák Z.: Theory of Rank Tests. Academia Praha (1967). MR 0229351
[4] Hušková M.: Limit theorems for rank statistics. Statist. Probab. Lett. 32 (1997), 45-55. MR 1439496
[5] Jarušková D.: Testing appearance of linear trend. J. Statist. Plann. Inference (1998), 70 263-276. MR 1649939
[6] Leadbetter M.R., Lindgren G., Rootzén H.: Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag Heidelberg (1983). MR 0691492
[7] Slabý A.: Behaviour of Some Rank Statistics for Detecting Changes. in Measuring Risk in Complex Stochastic Systems (proc. conf.), Berlin, 1999 (Franke J., Härdle W., Stahl G., Eds.), Springer-Verlag, Berlin, 2000, pp.161-172. MR 1752530
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