Summary
Let X 1 ,..., X n be a sequence of continuously distributed independent random variables. The normalized ranks R kn and sequential ranks S k , k=1,...,n, are defined by
The subject of the present paper is the asymptotic behavior, as n→∞, of the process
for a∈L 2 (0, 1), \(\int\limits_0^1 {{\text{adn}} = 0} \). For suitable a, the limiting law of that process is expressed as solution of a stochastic equation under the hypothesis of identically distributed X 1,..., X n as well as under a class of contiguous alternatives, which contains the occurrence of a change point in the series of measurements.
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Khmaladze, E.V., Parjanadze, A.M. Functional limit theorems for linear statistics from sequential ranks. Probab. Th. Rel. Fields 73, 585–595 (1986). https://doi.org/10.1007/BF00324854
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DOI: https://doi.org/10.1007/BF00324854