  Consider two random variables contaminated by two unknown transformations.
The aim of this paper is to test the equality of those transformations. Two
cases are distinguished: first, the two random variables have known
distributions. Second, they are unknown but observed before contaminations. We
propose a nonparametric test statistic based on empirical cumulative
distribution functions. Monte Carlo studies are performed to analyze the level
and the power of the test. An illustration is presented through a real data
set.
