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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.

Data driven efficient score tests for Poissonity

Inglot Tadeusz

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 1

115--126

New data driven score tests for testing goodness of fit of the Poisson distribution are proposed. They are direct applications of the general construction of data driven goodness-of-fit tests for composite hypotheses developed in Inglot et al. (1997). By a simulation study it is shown that these tests perform almost equally well as the best known solutions for standard alternatives and outperform them for more difficult alternatives.