8 / 2017-03-14 10:37:07

A Combined Procedure for Testing Multiple Hypotheses

There are numerous statistical and econometric testing problems that require
global tests of the intersection of individual hypotheses as well as
multiple tests of individual hypotheses. Tests such as MaxT or MinP tests
may have a considerable low global power compared with tests such as
likelihood ratio (LR) tests, hence leading to an erroneous conclusion of
false acceptance. This paper proposes hybrid tests that combine MaxT/MinP
tests and global tests such as LR tests. Hybrid tests are shown to have a
balanced power in global testing while retaining the ability for multiple
testing. We study two approaches for constructing hybrid tests. One is by
splitting the significance level between MaxT/MinP tests and global tests.
The other is constructed by taking the minimum of the $p$-values of global
tests and individual tests as the test statistic. In relation to multiple testing
further rejection of false individual
hypotheses are possible by allowing hybrid tests to proceed in a step-down
fashion of MaxT or MinP tests. Small-scale simulation studies and a real
data application are provided.