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Limit theorems for rank statistics. (English) Zbl 0933.62039
Summary: The purpose of this paper is to extend the weak asymptotic results for weighted partial sums of i.i.d. random variables to weighted partial sums of rank scores. These results then suggest various test procedures for the change point problem. The crucial tools in the proofs are martingale properties of a class of two-sample rank statistics and J. Hájek’s [Ann. Math. Stat. 32, 506–523 (1961; Zbl 0107.13404)] results on simple linear rank statistics.

##### MSC:
 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics 60F17 Functional limit theorems; invariance principles
##### Keywords:
rank statistics; weighted maxima; location model
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##### References:
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