Adaptive nonparametric tests for the two-sample scale problem under symmetry

The present paper considers two-sample tests for scale problem under symmetry without any assumption regarding the equality of medians. Two adaptive procedures are proposed-one is probabilistic while the other is deterministic. The proposed probabilistic approach is shown, by simulation studies, to maintain its significance level for various symmetric distributions and is found to be superior to the other existing competitors in terms of both robustness of size and power. Both the adaptive procedures are illustrated by using a real data. Some relevant asymptotic properties are also discussed.