Intermediate efficiency of tests
under heavy-tailed alternatives
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.
2010 AMS Mathematics Subject Classification: Primary 62G10; Secondary 62G20, 60F10.
Keywords and phrases: asymptotic relative efficiency, intermediate efficiency,
goodness-of-fit test, Kolmogorov--Smirnov test, Neyman--Pearson test, local alternatives, heavy-tailed alternatives, square integrable alternatives.