The problem of testing uniformity on [0, 1] against a clustering alternative, is considered. Naus has shown that the generalized likelihood ratio test yields the scan statistic $N(d)$. The asymptotic distribution of $N(d)$ under the null hypothesis of uniformity is considered herein, and related to the version of the scan statistic defined for points from a Poisson process. An application of the above yields distributional results for the supremum of a stationary Gaussian process with a correlation function that is tent-like in shape, until it flattens out at a constant negative value.
Publié le : 1980-08-14
Classification:
A particular Gaussian process,
asymptotic distribution,
clustering alternative distribution,
Poisson process,
scan statistic,
supremum distribution,
uniform distribution,
60G35,
62E20
@article{1176994669,
author = {Cressie, Noel},
title = {The Asymptotic Distribution of the Scan Statistic Under Uniformity},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 828-840},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994669}
}
Cressie, Noel. The Asymptotic Distribution of the Scan Statistic Under Uniformity. Ann. Probab., Tome 8 (1980) no. 6, pp. 828-840. http://gdmltest.u-ga.fr/item/1176994669/