Conditions to ensure the asymptotic normality of rank statistics having a scores generating function with finitely many jumps are obtained. These conditions are derived by studying rank statistics with a scores generating function $J$ such that $J(u) = 1$ or $0$ as $u \geqq s$ or $u < s$ for a fixed $s, 0 < s < 1$. No differentiability conditions are imposed on the underlying distribution functions at the jump points of the scores generating function.
Publié le : 1976-03-14
Classification:
Rank statistics,
asymptotic normality,
scores generating function with finitely many jumps,
two-sample problem,
62G10,
62E20
@article{1176343416,
author = {Shirahata, Shingo},
title = {On the Asymptotic Normality of Rank Statistics for The Two-Sample Problem},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 400-405},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343416}
}
Shirahata, Shingo. On the Asymptotic Normality of Rank Statistics for The Two-Sample Problem. Ann. Statist., Tome 4 (1976) no. 1, pp. 400-405. http://gdmltest.u-ga.fr/item/1176343416/