A multivariate version of Ghosh's T₃-plot to detect non-multinormality

Based on the theory of spherical distributions, a multivariate version of Ghosh (1996)'s T₃-plot (MT₃-plot) to detect non-multinormality is proposed. New critical bands for the MT₃-plot based on a Kolmogorov-Smirnov type statistic are recommended to substitute Ghosh's critical bands in multivariate cases. Monte Carlo study on the choice of the projection directions gives the conclusion that the power of the MT₃-plot based on the proposed Kolmogorov-Smirnov type statistic against severe non-multinormality is generally high regardless of high dimension if the projection direction is properly chosen. An application of the MT₃-plot to two real-life data sets verifies the efficiency of the MT₃ in finding evidence of non-multinormality in high-dimensional data analysis.