## The Annals of Statistics

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

Tiee-Jian Wu

#### 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

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