A class of empirical processes having the structure of $U$-statistics is considered. The weak convergence of the processes to a continuous Gaussian process is proved in weighted sup-norm metrics stronger than the uniform topology. As an application, a central limit theorem is derived for a very general class of non-parametric statistics.
Publié le : 1983-08-14
Classification:
Weak convergence,
sup-norm metrics,
empirical process,
dissociated random variables,
$U$-statistics,
order statistics,
$GL$-statistics,
asymptotic normality,
60F17,
62E20,
62G80
@article{1176993518,
author = {Silverman, B. W.},
title = {Convergence of a Class of Empirical Distribution Functions of Dependent Random Variables},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 745-751},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993518}
}
Silverman, B. W. Convergence of a Class of Empirical Distribution Functions of Dependent Random Variables. Ann. Probab., Tome 11 (1983) no. 4, pp. 745-751. http://gdmltest.u-ga.fr/item/1176993518/