Stochastic procedures are randomized statistical procedures which are functions of the observed sample and of one or more artificially constructed auxiliary samples. As the size of the auxiliary samples increases, a stochastic procedure becomes nearly nonrandomized. The stochastic test of this paper arises as a numerically feasible approximation to a natural minimum distance goodness-of-fit test for multivariate parametric models. The distance being minimized here is the half-space metric for probabilities on a Euclidean space. It is shown that the various approximations used in constructing the stochastic test and its critical values do not detract from its first-order asymptotic performance.
@article{1176347006,
author = {Beran, R. and Millar, P. W.},
title = {A Stochastic Minimum Distance Test for Multivariate Parametric Models},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 125-140},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347006}
}
Beran, R.; Millar, P. W. A Stochastic Minimum Distance Test for Multivariate Parametric Models. Ann. Statist., Tome 17 (1989) no. 1, pp. 125-140. http://gdmltest.u-ga.fr/item/1176347006/