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December, 1969 Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II
Vaclav Dupac, Jaroslav Hajek
Ann. Math. Statist. 40(6): 1992-2017 (December, 1969). DOI: 10.1214/aoms/1177697281


This is a straightforward continuation of Hajek (1968). We provide a further extension of the Chernoff-Savage (1958) limit theorem. The requirements concerning the scores-generating function are relaxed to a minimum: we assume that this function is a difference of two non-decreasing and square integrable functions. Thus, in contradistinction to Hajek (1968), we dropped the assumption of absolute continuity. The main results are accumulated in Section 2 without proofs. The proofs are given in Sections 4 through 7. Section 3 contains auxiliary results.


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Vaclav Dupac. Jaroslav Hajek. "Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II." Ann. Math. Statist. 40 (6) 1992 - 2017, December, 1969.


Published: December, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0193.17401
MathSciNet: MR253487
Digital Object Identifier: 10.1214/aoms/1177697281

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 6 • December, 1969
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