  The nonparametric test for change-point detection proposed by Gombay and
Horv\'ath is revisited and extended in the broader setting of empirical process
theory. The resulting testing procedure for potentially multivariate
observations is based on a sequential generalization of the functional
multiplier central limit theorem and on modifications of Gombay and Horv\'ath's
seminal approach that appears to improve the finite-sample behavior of the
tests. A large number of candidate test statistics based on processes indexed
by lower-left orthants and half-spaces are considered and their performance is
studied through extensive Monte Carlo experiments involving univariate,
bivariate and trivariate data sets. Finally, practical recommendations are
provided and the tests are illustrated on trivariate hydrological data.
