Invariant tests for multivariate normality: a critical review

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A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality (2005, methodology): “All of the above procedures, from the first three classes of tests of MVN, have been criticized by Baringhaus and Henze [14], Bogdan [26], Csörgö [28], Henze and Zirkler [40], and Henze [19] for lacking a formal proof of the property of consistency.”
A Generalization of Shapiro–Wilk's Test for Multivariate Normality (2009, methodology): “A Monte Carlo experiment was performed in order to assess the power performance of W ∗ in comparison with Mardia’s (1970) MS and MK, Henze and Zirkler’s (1990) T 5, Mudholkar’s et al.”
An Appraisal and Bibliography of Tests for Multivariate Normality (2004, background): “Although several reviews of the different methods exist (including Andrewset al., 1973; Gnanadesikan, 1977; Mardia, 1980; Koziol, 1986; Looney, 1995; Henze, 2002; Mudholkar & Srivastava, 2002), none of these reviews are completely comprehensive.”
The limit distribution of weighted $$L^2$$L2-goodness-of-fit statistics under fixed alternatives, with applications (2017, methodology): “As an example, we consider the now classical BHEP statistic for testing the hypothesis H0 that X has some non-degenerate d-variate normal distribution [see, e.g., Henze (2002), Section 6].”