We consider a sequence $\xi_1, \xi_2, \cdots$ of independent and identically distributed random observations. Let $\mu_n$ denote the empirical distribution for the sample $\{\xi_1, \cdots, \xi_n\}$. It is the aim of the present article to give a survey of various results in the theory of empirical distributions and empirical processes. Special emphasis is given to the developments of the last ten years.
Publié le : 1979-04-14
Classification:
60-02,
Empirical distribution,
empirical process,
Glivenko-Cantelli convergence,
LIL's for empirical processes,
weighted empirical process,
invariance principle,
rates of convergence,
random sample size,
strong approximation,
62D05,
60B10,
60F05,
60F10,
60F15,
60K99,
62E15,
60E20
@article{1176995085,
author = {Gaenssler, Peter and Stute, Winfried},
title = {Empirical Processes: A Survey of Results for Independent and Identically Distributed Random Variables},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 193-243},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995085}
}
Gaenssler, Peter; Stute, Winfried. Empirical Processes: A Survey of Results for Independent and Identically Distributed Random Variables. Ann. Probab., Tome 7 (1979) no. 6, pp. 193-243. http://gdmltest.u-ga.fr/item/1176995085/