How powerful are data driven score tests for uniformity

Tadeusz Inglot¹ ; Alicja Janic²

¹ Tadeusz Inglot Institute of Mathematics Polish Academy of Sciences and Institute of Mathematics and Informatics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
² Alicja Janic Institute of Mathematics and Informatics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Applicationes Mathematicae, Tome 36 (2009) no. 4, pp. 375-395

Résumé

We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some “optimal maximum test” attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the “optimal maximum test” with respect to the Neyman–Pearson tests, constructed separately for each alternative, in the Gaussian shift problem can be measured by the Shannon entropy of a prior distribution. This explains similar behaviour of the average power of our data driven tests.

Détail

DOI : 10.4064/am36-4-1

Keywords: construct class driven tests uniformity which have greater average power existing finite samples using simulation study these tests optimal maximum test attain average power close optimal bayes test finally prove middle range power function loss average power optimal maximum test respect neyman pearson tests constructed separately each alternative gaussian shift problem measured shannon entropy prior distribution explains similar behaviour average power driven tests