A two-sample test when data are contaminated

In this paper we consider the problem of testing whether two samples of contaminated data arise from the same distribution. Is is assumed that the contaminations are additive noises with known, or estimated moments. This situation can also be viewed as two signals observed before and after perturbations. The problem is then to test the equality of both perturbations. The test statistic is based on the polynomials moments of the difference between observations and noises. The test is very simple and allows one to compare two independent as well as two paired contaminated samples. A data driven selection is proposed to choose automatically the number of involved polynomials. We present a simulation study in order to investigate the power of the proposed test within discrete and continuous cases. Real-data examples are presented to illustrate the method. Copyright Springer-Verlag Berlin Heidelberg 2013