We establish strong and weak laws for Bahadur-Kiefer-type processes of the form $e_n + i_n$, where $i_n$ denotes the inverse of $e_n$. In particular, we provide a proof for the strong version of Theorem 1A of Kiefer (1970), together with similar results for renewal and partial sum processes.
Publié le : 1990-04-14
Classification:
Bahadur representation,
empirical and quantile processes,
partial sums and renewal processes,
strong laws,
weak laws,
order statistics,
weighted processes,
60F15,
60F05,
62G30,
60F17
@article{1176990852,
author = {Deheuvels, Paul and Mason, David M.},
title = {Bahadur-Kiefer-Type Processes},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 669-697},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990852}
}
Deheuvels, Paul; Mason, David M. Bahadur-Kiefer-Type Processes. Ann. Probab., Tome 18 (1990) no. 4, pp. 669-697. http://gdmltest.u-ga.fr/item/1176990852/