The infinitesimal robustness of tests against dependence
The robustness against dependence of nonparametric tests for the two-sample location problem
Nonparametric tests for the two-sample location problem are investigated. It is shown that the supremum of the size of any test can be arbitrarily close to 1. None of these tests is most robust against dependence.
Toward the best constant factor for the Rademacher-Gaussian tail comparison
It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c1 and c2 such that c2≈1.01 c1. A discussion of relative merits of this result versus limit theorems is given.