A large deviation result for signed linear rank statistics under the symmetry hypothesis
type: Item
instance of: scholarly article
title: A large deviation result for signed linear rank statistics under the symmetry hypothesis
zbMATH Open document ID: 0616.62021
author: Tiee-Jian Wu
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: This paper investigates the convergence of normalized signed linear rank statistics \(S_ n\) to the Gaussian distribution for i.i.d. random variables the distribution of which is continuous and symmetric about zero. It considers the uniform convergence of distribution functions over intervals going to infinity slower than \(n^{1/4}:\) this can be called ''mean deviation'' but not large deviation theorem. The author considers unbounded score functions and improves the result of \textit{M. Seoh, S. Ralescu} and \textit{M. L. Puri} [Ann. Probab. 13, 115-125 (1985; Zbl 0558.62019)].
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3998968
zbMATH Keywords: Cramér type large deviation theorem
zbMATH Keywords: symmetric distributions
zbMATH Keywords: deviation from normality
zbMATH Keywords: signed linear rank statistics
zbMATH Keywords: Gaussian distribution
zbMATH Keywords: mean deviation
zbMATH Keywords: unbounded score functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349955
OpenAlex ID: W1969834184
DOI: 10.1214/AOS/1176349955
description: scientific article; zbMATH DE number 3998968