Any triangular array of row independent $\mathrm{rv}$'s having continuous $\mathrm{df}$'s can be transformed naturally so that the empirical and quantile processes of the resulting $\mathrm{rv}$'s are relatively compact. Moreover, convergence (to a necessarily normal process) takes place if and only if a simple covariance function converges pointwise. Using these results we derive the asymptotic normality of linear combinations of functions of order statistics of non-i.i.d. $\mathrm{rv}$'s in the case of bounded scores.
Publié le : 1973-01-14
Classification:
Convergence of non-i.i.d. empirical processes,
asymptotic normality of functions of non-i.i.d. order statistics,
62G30,
60B10,
62E20
@article{1193342391,
author = {Shorack, Galen R.},
title = {Convergence of Reduced Empirical and Quantile Processes with Application to Functions of Order Statistics in the Non-I.I.D. Case},
journal = {Ann. Statist.},
volume = {1},
number = {2},
year = {1973},
pages = { 146-152},
language = {en},
url = {http://dml.mathdoc.fr/item/1193342391}
}
Shorack, Galen R. Convergence of Reduced Empirical and Quantile Processes with Application to Functions of Order Statistics in the Non-I.I.D. Case. Ann. Statist., Tome 1 (1973) no. 2, pp. 146-152. http://gdmltest.u-ga.fr/item/1193342391/