Null distribution of the sum of squared z-transforms in testing complete independence

Brien et al. (1984, Biometrika, 71, 545–554; 1988, Biometrika, 75, 469–476) have proposed, illustrated and discussed advantages of using Fisher's z-transforms for analyzing correlation structures of multinormal data. Chen and Mudholkar (1988, Austral. J. Statist., 31, 105–110) have studied the sum of squared z-transforms of sample correlations as a test statistic for complete independence. In this paper Brown's (1987, Ann. Probab., 15, 416–422) graph-theoretic characterization of the dependence structure of sample correlations is used to evaluate moments of the test statistic. These moments are then used to approximate its null distribution accurately over a broad range of parameters, including the case where the population dimension exceeds the sample size.