The Annals of Statistics

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

Tiee-Jian Wu

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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


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