This paper presents a multivariate Kolmogorov-Smirnov (MVKS) goodness of fit test for
multivariate normality. The proposed test is based on the difference between the empirical
distribution function and the theoretical distribution function. While calculating them in
multivariate case, the problem is that the variables cannot be distribution-free as in the
univariate case. Firstly, the variables are made independent to solve this problem and
the Rosenblatt transform is applied for independence of variates. Then the theoretical
and empirical distribution values are calculated and the MVKS test statistic is computed.
It provides an easy calculation for d-dimensional data by using the same algorithm and
critical table values. This paper demonstrates the effectiveness of the MVKS for different dimensions with a simulation study which also includes the comparison of the MVKS
critical tables with univariate Kolmogorov-Smirnov (KS) critical table and the power comparisons of the MVKS (bivariate case) against with the existing bivariate normality tests.
Lastly, the MVKS is applied to two different multivariate data sets to confirm that it
achieves consistent, accurate and correct results.