Any triangular array of row independent random vectors with continuous df's has a standard reduction to random vectors with values in the unit cube. The reduced empirical process belonging to the transformed random vectors is always relatively compact. Weak convergence to a (necessarily Gaussian) process holds iff the corresponding covariance kernel converges pointwise.
Publié le : 1975-03-14
Classification:
Non. i.i.d. random-vectors,
convergence of the empirical process,
60B10,
60G15
@article{1176343084,
author = {Neuhaus, Georg},
title = {Convergence of the Reduced Empirical Process for Non-I.I.D. Random Vectors},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 528-531},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343084}
}
Neuhaus, Georg. Convergence of the Reduced Empirical Process for Non-I.I.D. Random Vectors. Ann. Statist., Tome 3 (1975) no. 1, pp. 528-531. http://gdmltest.u-ga.fr/item/1176343084/