Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for a broad class of one-sample rank order statistics, weak convergence to Brownian motion processes is studied here. A simple proof of the asymptotic normality of these statistics for random sample sizes is also presented. Some asymptotic results on renewal theory for one-sample rank order statistics are derived.
Publié le : 1974-01-14
Classification:
Brownian motion processes,
invariance principles,
martingales,
one-sample rank order statistics,
random sample sizes,
renewal theory,
weak convergence,
60B10,
62G99
@article{1176342612,
author = {Sen, Pranab Kumar},
title = {The Invariance Principle for One-Sample Rank-Order Statistics},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 49-62},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342612}
}
Sen, Pranab Kumar. The Invariance Principle for One-Sample Rank-Order Statistics. Ann. Statist., Tome 2 (1974) no. 1, pp. 49-62. http://gdmltest.u-ga.fr/item/1176342612/