The Annals of Statistics

On the Asymptotic Normality of Rank Statistics for The Two-Sample Problem

Shingo Shirahata

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Abstract

Conditions to ensure the asymptotic normality of rank statistics having a scores generating function with finitely many jumps are obtained. These conditions are derived by studying rank statistics with a scores generating function $J$ such that $J(u) = 1$ or $0$ as $u \geqq s$ or $u < s$ for a fixed $s, 0 < s < 1$. No differentiability conditions are imposed on the underlying distribution functions at the jump points of the scores generating function.

Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 400-405.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343416

Digital Object Identifier
doi:10.1214/aos/1176343416

Mathematical Reviews number (MathSciNet)
MR405672

Zentralblatt MATH identifier
0325.62035

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62E20: Asymptotic distribution theory

Keywords
Rank statistics asymptotic normality scores generating function with finitely many jumps two-sample problem

Citation

Shirahata, Shingo. On the Asymptotic Normality of Rank Statistics for The Two-Sample Problem. Ann. Statist. 4 (1976), no. 2, 400--405. doi:10.1214/aos/1176343416. https://projecteuclid.org/euclid.aos/1176343416


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