A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality

A Monte Carlo power study of 10 multivariate normality goodness-of-fit tests is presented. First, multivariate goodness-of-fit methods and non-normal alternatives are classified according to their characteristics. Then, a measurement tool is defined, validated, and used to assess the performance of the methods, which are then ranked by type of alternative they best detect. Finally, Monte Carlo-derived empirical critical values for the 8 procedures, valid when samples are too small to invoke asymptotic theory, are provided.