We propose a class of ratio tests that is applicable whenever a cumulation (of transformed) data is asymptotically normal upon appropriate normalization. All it requires is the orthonormal expansion using the Karhunen-Loeve [KL] theorem, which is employed to compute weighted averages of the...

The inverse normal method, which is used to combine P-values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, Biometrical Journal, Vol....