## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 4 (1977), 658-670.

### The Rate of Convergence of Simple Linear Rank Statistics Under Hypothesis and Alternatives

#### Abstract

Convergence rates for distributions of simple linear rank statistics are investigated. Both the null hypothesis and near alternatives are considered. The method of proof consists in approximating the characteristic function of the statistic by that of a sum of independent random variables and then applying standard tools.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 4 (1977), 658-670.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343890

**Digital Object Identifier**

doi:10.1214/aos/1176343890

**Mathematical Reviews number (MathSciNet)**

MR458711

**Zentralblatt MATH identifier**

0365.62039

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 62G10: Hypothesis testing

**Keywords**

Simple linear rank statistics rate of convergence distribution free tests contiguous alternatives

#### Citation

Huskova, Marie. The Rate of Convergence of Simple Linear Rank Statistics Under Hypothesis and Alternatives. Ann. Statist. 5 (1977), no. 4, 658--670. doi:10.1214/aos/1176343890. https://projecteuclid.org/euclid.aos/1176343890