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Intermediate Efficiency of Tests Under Heavy-Tailed Alternatives

Inglot Tadeusz

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 2

331--348

We show that for local alternatives which are not square integrable the intermediate (or Kallenberg) efficiency of the Neyman–Pearson test for uniformity with respect to the classical Kolmogorov–Smirnov test is infinite. By contrast, for square integrable local alternatives the intermediate efficiency is finite and can be explicitly calculated.

Asymptotic behaviour of linear rank statistics for the two-sample problem

Inglot T.

Probability and Mathematical Statistics

2012

Vol. 32, Fasc. 1

93--116

Applying the strong approximation technique we present a unified approach to asymptotic results for multivariate linear rank statistics for the two-sample problem. We reprove asymptotic normality of these statistics under the null hypothesis and under local alternatives convergent at a moderate rate to the null hypothesis. We also provide a moderate deviation theorem for these statistics under the null hypothesis. Proofs are short and use natural argumentation.