Some two-dimensional time-parameter stochastic processes are constructed from a sequence of linear rank statistics by considering their projections on the spaces generated by the (double) sequence of anti-ranks. Under appropriate regularity conditions, it is shown that these processes weakly converge to Brownian sheets in the Skorokhod $J_1$-topology on the $D^2\lbrack 0, 1 \rbrack$ space. This unifies and extends earlier one-dimensional invariance principles for linear rank statistics to the two-dimensional case. The case of contiguous alternatives is treated briefly.
Publié le : 1976-02-14
Classification:
Brownian sheet,
contiguity,
$D^2\lbrack 0, 1 \rbrack$ space,
$J_1$-topology,
linear rank statistics,
permutational central limit theorems,
tightness,
two-dimensional stochastic processes and weak convergence,
60B10,
60F05,
62G99
@article{1176996177,
author = {Sen, Pranab Kumar},
title = {A Two-Dimensional Functional Permutational Central Limit Theorem for Linear Rank Statistics},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 13-26},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996177}
}
Sen, Pranab Kumar. A Two-Dimensional Functional Permutational Central Limit Theorem for Linear Rank Statistics. Ann. Probab., Tome 4 (1976) no. 6, pp. 13-26. http://gdmltest.u-ga.fr/item/1176996177/