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.
Publié le : 1990-09-14
Classification:
Berry-Esseen bound,
rate of convergence,
signed linear rank statistic,
discontinuous score generating function,
62E20,
60F05,
62G10
@article{1176347763,
author = {Seoh, Munsup},
title = {Berry-Esseen-Type Bounds for Signed Linear Rank Statistics with a Broad Range of Scores},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 1483-1490},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347763}
}
Seoh, Munsup. Berry-Esseen-Type Bounds for Signed Linear Rank Statistics with a Broad Range of Scores. Ann. Statist., Tome 18 (1990) no. 1, pp. 1483-1490. http://gdmltest.u-ga.fr/item/1176347763/