We derive large deviation approximations to boundary crossing probabilities for a class of point processes which can be approximated locally as Poisson processes. In the special case of empirical processes, we are able to obtain second order correction terms. The methods are applied to Kolmogorov-Smirnov testing, where we are able to obtain accurate approximations to the significance level when the null hypothesis is an exponential family with unknown nuisance parameters.
Publié le : 1992-02-14
Classification:
Boundary crossing,
empirical process,
change point,
Kolmogorov-Smirnov test,
point process,
Poisson process,
60G55,
60F10,
60G40
@article{1177005778,
author = {Loader, Clive R.},
title = {Boundary Crossing Probabilities for Locally Poisson Processes},
journal = {Ann. Appl. Probab.},
volume = {2},
number = {4},
year = {1992},
pages = { 199-228},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005778}
}
Loader, Clive R. Boundary Crossing Probabilities for Locally Poisson Processes. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp. 199-228. http://gdmltest.u-ga.fr/item/1177005778/