Based on the well known Karhunen–Loève expansion, it can be shown that many omnibus tests lack power against “high frequency” alternatives. The smooth tests of  Neyman (1937) may be employed to circumvent this power deficiency problem. Yet, such tests may be difficult to compute in many...

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...