A robustified Jarque-Bera test for multivariate normality

•The Jarque-Bera test and its modifications are generalized to multivariate versions.•Orthogonalization or an empirical standardization of data is used for generalization.•Power of the suggested statistics is compared against the various alternative distributions.

The Jarque-Bera test and its modifications for univariate normality are generalized to multivariate versions using orthogonalization or an empirical standardization of data. Each modification has strength against some alternative distributions, and all modified test statistics show comparable power to the multivariate Jarque-Bera test.