## The Annals of Statistics

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

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

#### 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