Annals of Statistics

Berry-Esseen-Type Bounds for Signed Linear Rank Statistics with a Broad Range of Scores

Munsup Seoh

Full-text: Open access

Abstract

The Berry-Esseen-type bounds of order $N^{-1/2}$ for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.

Article information

Source
Ann. Statist., Volume 18, Number 3 (1990), 1483-1490.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347763

Digital Object Identifier
doi:10.1214/aos/1176347763

Mathematical Reviews number (MathSciNet)
MR1062722

Zentralblatt MATH identifier
0705.62026

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 60F05: Central limit and other weak theorems 62G10: Hypothesis testing

Keywords
Berry-Esseen bound rate of convergence signed linear rank statistic discontinuous score generating function

Citation

Seoh, Munsup. Berry-Esseen-Type Bounds for Signed Linear Rank Statistics with a Broad Range of Scores. Ann. Statist. 18 (1990), no. 3, 1483--1490. doi:10.1214/aos/1176347763. https://projecteuclid.org/euclid.aos/1176347763


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