Asymptotic correct correlation tests in model validation

It is well-known that correlation tests may give true significance levels that differ significantly from the desired ones, the tests are less inclined to reject the null hypothesis when second-hand data are used compared with how they are designed to behave, and the situation is the opposite for “fresh” data. The reason is that the tests are based on the assumption that the limit model (corresponding to infinite data) is available. In this paper, we propose a methodology to design correlation tests that avoid this artifact. This leads to tests of higher order correlations