The sample paths of cumulative sums of induced order statistics obtained from $n$ independent two-dimensional random vectors, when appropriately normalized, converge weakly (as $n$ increases indefinitely) to the sum of a Brownian motion with time change and an integrated Brownian bridge which is independent of the Brownian motion. Applications in regression analysis are given.
Publié le : 1976-05-14
Classification:
Induced order statistics,
regression analysis,
weak convergence,
Brownian motion,
62E20
@article{1176343468,
author = {Bhattacharya, P. K.},
title = {An Invariance Principle in Regression Analysis},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 621-624},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343468}
}
Bhattacharya, P. K. An Invariance Principle in Regression Analysis. Ann. Statist., Tome 4 (1976) no. 1, pp. 621-624. http://gdmltest.u-ga.fr/item/1176343468/