A two-dimensional Cramér–von Mises test for the two-sample problem with dispersion alternatives

Ferger Dietmar

Statistics & Risk Modeling, 2004, vol. 22, issue 2, 131-151

Abstract: We consider the two-sample problem with dispersion alternatives. Starting with a sufficient characterization of the alternative by means of two integrals we come up with a test which is based on the empirical counterparts of the integrals. Especially the critical region is now the inverse image of an infinite rectangle in ℝ2. The common limit distribution of the empirical integrals is determined under the hypothesis of randomness and under a broad class of nonparametric local alternatives. In each case it turns out to be normal. It enables the construction of an asymptotic level-α test, which is consistent on the alternative. In addition we are able to make local power investigations. In our example the new test is superior to the classical Cramér–von Mises test.

Date: 2004
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DOI: 10.1524/stnd.22.2.131.49128

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