Key points are not available for this paper at this time.
The comparison of several powerful tests for multinormality is appropriate in order to know the test(s) to use under different alternatives to multivariate normality. The aim of this work is to compare the power of some notable powerful multivariate normality tests for different combinations of sample size and variable dimension. The multivariate normality tests considered were Henze and Zirkler test (HZ-test), Szekely and Rizzo energy test (SR-test), Madukaife and Okafor test (MO-test), Henze and Jimenez-Gamero test (HJG-test), Dorr, Ebner and Henze test (DEHU-test), Henze and Visagie test (HV-test), Ebner, Henz and Strieder test (EHS-test), and Madukaife test (M-test). The study took into account 5 multivariate distributions, 5 different sample sizes (n = 10, 20, 30, 40 and 50) and 5 different variable dimensions (d = 2, 3, 5, 7 and 9). The multivariate distributions considered were multivariate normal, multivariate t, multivariate uniform, multivariate Laplace, and multivariate exponential distributions. For 2 ≤ d ≤ 9, HZ-test, HJG-test, DEHU-test, EHS-test, HV-test, M-test, MO-test and SR-test maintained relevant type-I-error rate under multivariate normal distribution. Under the alternative distributions of multivariate t and Laplace, the MO-test outperformed all the multivariate normality tests at n = 10, 20, 30, 40 and 50 regardless of the variable dimension while HZ-test outperformed all the multivariate normality tests at n = 10, 20, 30, 40 and 50 regardless of the variable dimension in multivariate uniform distribution. Hence, the MO-test is recommended over HZ-test, HJG-test, DEHU-test, EHS-test, HV-test, M-test and SR-test when the data are asymmetric.
Chukwudozie et al. (Sun,) studied this question.