We present a solution to the goodness-of-fit problem for multivariate observations, using the innovation process for the (sequential) empirical distribution function with respect to a conveniently chosen linear ordering or scanning system in $R^m$.
@article{1176351051,
author = {Khmaladze, E. V.},
title = {An Innovation Approach to Goodness-of-Fit Tests in $R^m$},
journal = {Ann. Statist.},
volume = {16},
number = {1},
year = {1988},
pages = { 1503-1516},
language = {en},
url = {http://dml.mathdoc.fr/item/1176351051}
}
Khmaladze, E. V. An Innovation Approach to Goodness-of-Fit Tests in $R^m$. Ann. Statist., Tome 16 (1988) no. 1, pp. 1503-1516. http://gdmltest.u-ga.fr/item/1176351051/