Tests of fit that assume i.i.d. observations may be affected by dependence among the observations. This effect is studied for the Pearson chi squared test when the data form a stationary stochastic process. The general form of asymptotic distribution theory under the null hypothesis is outlined and examples are given. For testing fit to a specified normal law, it is shown that when observations come from a quite general class of Gaussian stationary processes, positive correlation among the observations is confounded with lack of normality.
Publié le : 1982-12-14
Classification:
Chi squared tests,
stationary stochastic proceses,
goodness of fit,
62G10,
62M99
@article{1176345981,
author = {Moore, David S.},
title = {The Effect of Dependence on Chi Squared Tests of Fit},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 1163-1171},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345981}
}
Moore, David S. The Effect of Dependence on Chi Squared Tests of Fit. Ann. Statist., Tome 10 (1982) no. 1, pp. 1163-1171. http://gdmltest.u-ga.fr/item/1176345981/