## The Annals of Statistics

- Ann. Statist.
- Volume 14, Number 2 (1986), 774-780.

### A Large Deviation Result for Signed Linear Rank Statistics Under the Symmetry Hypothesis

#### Abstract

A Cramer type large deviation theorem for signed linear rank statistics under the symmetry hypothesis is obtained. The theorem is proved for a wide class of scores covering most of the commonly used ones (including the normal scores). Furthermore, the optimal range $0 < x \leq o(n^{1/4})$ can be obtained for bounded scores, whereas the range $0 < x \leq o(n^\delta), \delta \in (0, \frac{1}{4})$ is obtainable for many unbounded ones. This improves the earlier result under the symmetry hypothesis in Seoh, Ralescu, and Puri (1985).

#### Article information

**Source**

Ann. Statist., Volume 14, Number 2 (1986), 774-780.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176349955

**Digital Object Identifier**

doi:10.1214/aos/1176349955

**Mathematical Reviews number (MathSciNet)**

MR840531

**Zentralblatt MATH identifier**

0616.62021

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F10: Large deviations

Secondary: 62E20: Asymptotic distribution theory

**Keywords**

Signed linear rank statistics score generating function large deviation probabilities

#### Citation

Wu, Tiee-Jian. A Large Deviation Result for Signed Linear Rank Statistics Under the Symmetry Hypothesis. Ann. Statist. 14 (1986), no. 2, 774--780. doi:10.1214/aos/1176349955. https://projecteuclid.org/euclid.aos/1176349955