The Annals of Mathematical Statistics

Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II

Vaclav Dupac and Jaroslav Hajek

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 40, Number 6 (1969), 1992-2017.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177697281

Digital Object Identifier
doi:10.1214/aoms/1177697281

Mathematical Reviews number (MathSciNet)
MR253487

Zentralblatt MATH identifier
0193.17401

JSTOR
links.jstor.org

Citation

Dupac, Vaclav; Hajek, Jaroslav. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II. Ann. Math. Statist. 40 (1969), no. 6, 1992--2017. doi:10.1214/aoms/1177697281. https://projecteuclid.org/euclid.aoms/1177697281


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